16
Global Sourcing
and Procurement
Learning Objectives
LO 16–1
LO 16–2
LO 16–3
LO 16–4
Explain what strategic sourcing is.
Explain why companies outsource processes.
Analyze the total cost of ownership.
Evaluate sourcing performance.
THE FACTORYLESS GOODS PRODUCERS
Consider a company like Apple Inc. and its iPhone and iPad. Apple handles every part
of making its products except the actual fabrication. Currently, Apple outsources the
production of many of its products to Taiwan’s Hon Hai Precision Industry. Hon Hai,
which is better known as Foxconn, draws 40 to 50 percent of its revenue from assembling Apple products.
As many industries have become
global suppliers, this type of global outsourcing has become common for clothing, most retail household products,
furniture, and computers. These factoryless goods producers do most of the
functions of manufacturing, and in many
cases, design the product and oversee
distribution.
Much of the attraction for this arrangement is the traditionally low labor costs
in Chinese factories. Because labor cost
has recently surged in China, outsourcing specialists such as Foxconn have
diversified their operations to other
low-wage countries, including Vietnam,
Indonesia, Turkey, Brazil, Mexico, and
Hungary.
© Mick Ryan/Getty Images RF
402
Global Sourcing and Procurement
Chapter 16
403
STR ATEGIC SOURCING
Strategic sourcing is the development and management of supplier relationships to acquire
goods and services in a way that aids in achieving the immediate needs of the business. In the
past, the term sourcing was just another term for purchasing, a corporate function that financially was important but strategically was not the center of attention. Today, as a result of globalization and inexpensive communications technology, the basis for competition is changing.
A firm is no longer constrained by the capabilities it owns; what matters is its ability to make
the most of available capabilities, whether they are owned by the firm or not. Outsourcing
is so sophisticated that even core functions such as engineering, research and development,
manufacturing, information technology, and marketing can be moved outside the firm.
Sourcing activities can vary greatly and depend on the item being purchased. Exhibit 16.1
maps different processes for sourcing or purchasing an item. The term sourcing implies a
more complex process suitable for products that are strategically important. Purchasing processes that span from a simple “spot” or one-time purchase to a long-term strategic alliance
are depicted on the diagram. The diagram positions a purchasing process according to the
specificity of the item, contract duration, and intensity of transaction costs.
Specificity refers to how common the item is and, in a relative sense, how many substitutes
might be available. For example, blank DVD disks are commonly available from many different vendors and would have low specificity. A custom-made envelope that is padded and
specially shaped to contain a specific item that is to be shipped would be an example of a
high-specificity item.
Commonly available products can be purchased using a relatively simple process. For lowvolume and inexpensive items purchased during the regular routine of work, a firm may order
from an online catalog. Often, these online catalogs are customized for a customer. Special
user identifications can be set up to authorize a customer’s employees to purchase certain
groups of items, with limits on how much they can spend. Other items require a more complex process.
A request for proposal (RFP) is commonly used for purchasing items that are more complex or expensive and where there may be a number of potential vendors. A detailed information packet describing what is to be purchased is prepared and distributed to potential vendors.
The vendor then responds with a detailed proposal of how the company intends to meet the
terms of the RFP. A request for bid or reverse auction is similar in terms of the information
packet needed. A major difference is how the bid price is negotiated. In the RFP, the bid is
included in the proposal, whereas in a request for bid or reverse auction, vendors actually bid
on the item in real time and often using Internet software.
exhibit 16.1
Short
The Sourcing/Purchasing Design Matrix
Low
Request for
proposal
Spot
purchase
Request for bid
and
reverse auctions
Contract
duration
Electronic
catalog
Strategic
alliance
Long
High
Specificity
Transaction costs
Vendor
managed
inventory
Low
High
LO 16–1
Explain what strategic
sourcing is.
Strategic sourcing
The development and
management of supplier
relationships to acquire
goods and services in a
way that aids in achieving
the needs of a business.
Sourcing
A process suitable for
procuring products that are
strategically important to
the firm.
Specificity
Refers to how commonly
available the material is
and whether substitutes
can be used.
Request for proposal
A solicitation that asks for
a detailed proposal from
a vendor interested in
supplying an item.
404
Section 3
Supply Chain Processes
Vendor-managed inventory is when a customer actually allows the supplier to manage the inventory policy
of an item or group of items for them. In this case, the
supplier is given the freedom to replenish the item as they
see fit. Typically, there are some constraints related to the
maximum that the customer is willing to carry, the required
service levels, and other billing transaction processes.
Selecting the proper process depends on minimizing the
balance between the supplier’s delivered costs of the item
over a period of time, say a year, and the customer’s costs
of managing the inventory. This is discussed later in the
chapter in the context of the “total cost of ownership” for
a purchased item.
T h e Bu llwh ip E f f ect
In many cases, there are adversarial relations between supply chain partners, as well as dysfunctional industry practices such as a reliance on price promotions. Consider the
common food industry practice of offering price promotions every January on a product. Retailers respond to the
Instead of sending purchase orders, customers
price cut by stocking up, in some cases buying a year’s
electronically send daily demand information to the
supply—a practice the industry calls forward buying.
supplier. The supplier generates replenishment orders for
Nobody wins in the deal. Retailers have to pay to carry the
the customer based on this demand information.
year’s supply, and the shipment bulge adds cost through© Charlie Westerman/Getty Images
out the supplier’s system. For example, the supplier plants
must go on overtime starting in October to meet the bulge.
Vendor-managed
Even
the
vendors
that
supply
the
manufacturing
plants are affected because they must quickly
inventory
react
to
the
large
surge
in
raw
material
requirements.
When a customer allows
The impact of these types of practices has been studied at companies such as Procter &
the supplier to manage the
Gamble. Exhibit 16.2 shows typical order patterns faced by each node in a supply chain that
inventory policy of an item
or group of items.
consists of a manufacturer, a distributor, a wholesaler, and a retailer. In this case, the demand
is for disposable baby diapers. The retailer’s orders to the wholesaler display greater variForward buying
ability than the end-consumer sales; the wholesaler’s orders to the manufacturer show even
A term that refers to when
more oscillations; and, finally, the manufacturer’s orders to its suppliers are the most volatile.
a customer, responding to
This phenomenon of variability magnification as we move from the customer to the producer
a promotion, buys far in
in the supply chain is often referred to as the bullwhip effect. The effect indicates a lack of
advance of when an item
synchronization among supply chain members. Even a slight change in consumer sales ripples
will be used.
backward in the form of magnified oscillations upstream, resembling the result of a flick of
a bullwhip handle. Because the supply patterns do not match the demand patterns, invenBullwhip effect
tory accumulates at various stages, and shortages and delays occur at others. This bullwhip
The variability in demand
effect has been observed by many firms in numerous industries, including Campbell Soup and
is magnified as we move
from the customer to the
Procter & Gamble in consumer products; Hewlett-Packard, IBM, and Motorola in electronics;
producer in the supply
General Motors in automobiles; and Eli Lilly in pharmaceuticals.
chain.
Campbell Soup pioneered a program called continuous replenishment that typifies what
many manufacturers are doing to smooth the flow of materials through their supply chain.
Continuous
Here is how the program works. Campbell establishes electronic data interchange (EDI)
replenishment
links with retailers and offers an “everyday low price” that eliminates discounts. Every
A program for
morning, retailers electronically inform the company of their demand for all C
­ ampbell prodautomatically supplying
ucts
and
of
the
level
of
inventories
in
their
distribution
centers.
Campbell
uses
that informagroups of items to a
tion to forecast future demand and to determine which products require replenishment based
customer on a regular
basis.
on upper and lower inventory limits previously established with each supplier. Trucks leave
the Campbell shipping plant that afternoon and arrive at the retailers’ distribution centers
with the required replenishments the same day. Using this system, Campbell can cut the
retailers’ inventories, which under the old system averaged four weeks of supply, to about
two weeks of supply.
Global Sourcing and Procurement
ex hibit 16.2
20
15
15
Order Quantity
Order Quantity
Retailer’s Orders to Wholesaler
20
10
5
10
5
0
Time
20
20
15
15
10
5
Time
Time
Manufacturer’s Orders to Supplier
Order Quantity
Order Quantity
Wholesaler’s Orders to Manufacturer
0
405
Increasing Variability of Orders Up the Supply Chain
Consumer Sales
0
Chapter 16
10
5
0
Time
This solves some problems for Campbell Soup, but what are the advantages for the retailer?
Most retailers figure that the cost to carry the inventory of a given product for a year equals at
least 25 percent of what they paid for the product. A two-week inventory reduction represents
a cost savings equal to nearly 1 percent of sales. The average retailer’s profits equal about
2 percent of sales, so this saving is enough to increase profits by 50 percent. Because the
retailer makes more money on Campbell products delivered through continuous replenishment, it has an incentive to carry a broader line of them and to give them more shelf space.
Campbell Soup found that after it introduced the program, sales of its products grew twice as
fast through participating retailers as they did through other retailers.
Supply Chain Uncertainty Framework
The supply chain uncertainty framework (Exhibit 16.3) is designed to help managers understand the nature of demand for their products and then devise the supply chain that can
best satisfy that demand. Many aspects of a product’s demand are important—for example,
product life cycle, demand predictability, product variety, and market standards for lead
times and service. Products can be categorized as either primarily functional or primarily
innovative. Because each category requires a distinctly different kind of supply chain, the
root cause of supply chain problems is a mismatch between the type of product and type of
supply chain.
Functional products include the staples that people buy in a wide range of retail outlets,
such as grocery stores and gas stations. Because such products satisfy basic needs, which do
not change much over time, they have stable, predictable demand and long life cycles. But
their stability invites competition, which often leads to low profit margins. Specific criteria
for identifying functional products include the following: product life cycle of more than two
years, contribution margin of 5 to 20 percent, only 10 to 20 product variations, an average
Functional products
Staples that people buy
in a wide range of retail
outlets, such as grocery
stores and gas stations.
406
Supply Chain Processes
Section 3
Innovative products
Products such as
fashionable clothes and
personal computers that
typically have a life cycle of
just a few months.
Stable supply process
A process where the
underlying technology is
stable.
Evolving supply
process
A process where the
underlying technology
changes rapidly.
exhibit 16.3
forecast error at time of production of only 10 percent, and a lead time for make-to-order
products of from six months to one year.
To avoid low margins, many companies introduce innovations in fashion or technology to
give customers an additional reason to buy their products. Fashionable clothes and personal
computers are good examples. Although innovation can enable a company to achieve higher
profit margins, the very newness of the innovative products makes demand for them unpredictable. These innovative products typically have a life cycle of just a few months. Imitators
quickly erode the competitive advantage that innovative products enjoy, and companies are
forced to introduce a steady stream of newer innovations. The short life cycles and the great
variety typical of these products further increase unpredictability. Exhibit 16.3 summarizes
the differences between functional and innovative products.
We expand on this idea by focusing on the “supply” side of the supply chain. While the
Supply Chain uncertainty framework captures important demand characteristics, there are
uncertainties revolving around the supply side that are equally important drivers for the right
supply chain strategy.
A stable supply process is where the manufacturing process and the underlying technology
are mature and the supply base is well established. In contrast, an evolving supply process is
where the manufacturing process and the underlying technology are still under early development and are rapidly changing. As a result, the supply base may be limited in both size and
experience. In a stable supply process, manufacturing complexity tends to be low or manageable. Stable manufacturing processes tend to be highly automated, and long-term supply contracts are prevalent. In an evolving supply process, the manufacturing process requires a lot of
fine-tuning and is often subject to breakdowns and uncertain yields. The supply base may not
be reliable, because the suppliers themselves are going through process innovations. Exhibit
16.3 summarizes some of the differences between stable and evolving supply processes.
While functional products tend to have a more mature and stable supply process, that is not
always the case. For example, the annual demand for electricity and other utility products in a
locality tends to be stable and predictable, but the supply of hydroelectric power, which relies
on rainfall in a region, can be erratic year by year. Some food products also have a very stable
demand, but the supply (both quantity and quality) of the products depends on yearly weather
conditions. Similarly, there are also innovative products with a stable supply process. Fashion
apparel products have a short selling season and their demand is highly unpredictable. However, the supply process is very stable, with a reliable supply base and a mature manufacturing
process technology. Exhibit 16.4 gives some examples of products that have different demand
and supply uncertainties.
In most cases, it is more challenging to operate a supply chain that is in the right column
of Exhibit 16.4 than in the left column, and similarly it is more challenging to operate a supply chain that is in the lower row of Exhibit 16.4 than in the upper row. Before setting up a
supply chain strategy, it is necessary to understand the sources of the underlying uncertainties and explore ways to reduce these uncertainties. If it is possible to move the uncertainty
Product and Process Uncertainty Characteristics
Product (Demand)
Characteristics
Functional
Innovative
Demand
Predictable
Unpredictable
Product Life
Long
Short
Inventory Value
Low
Product Variety
Volume
Stock-out Cost
Manufacturing (Supply) Process
Characteristics
Stable
Evolving
Breakdowns
Few
Higher
Process Yield
High
Lower
High
Quality Problems
Few
More
Low
High
Supply Sources
Many
Few
High
Low
Process Changes
Few
Many
Low
High
Lead Time
Dependable
Difficult to predict
Based on research conducted by Marshall Fisher (Wharton School of Business, University of Pennsylvania).
Global Sourcing and Procurement
ex hibit 16.4
Chapter 16
Supply Chain Uncertainty Framework
Product (Demand) Characteristics
Manufacturing (Supply) Process
Characteristics
Functional
Innovative
Stable
Efficient Supply Chain
Grocery, basic apparel, food, oil and gas
Responsive Supply Chain
Fashion apparel, low-end computers,
seasonal products
Evolving
Risk-Hedging Supply Chain
Hydroelectric power, food dependent on
weather
Agile Supply Chain
Cellphones, high-end computers,
semiconductors
Based on research conducted by Hau Lee (Stanford University).
characteristics of the product from the right column to the left or from the lower row to the
upper, then the supply chain performance will improve.
Using the supply and demand characteristics discussed so far, four types of supply chain
strategies, as shown in Exhibit 16.4, are possible. Information technologies play an important
role in shaping such strategies.
∙
∙
∙
∙
Efficient supply chains These are supply chains that utilize strategies aimed at creating the highest levels of cost efficiency. For such efficiencies to be achieved, non–valueadded activities should be eliminated, scale economies should be pursued, optimization
techniques should be deployed to get the best capacity utilization in production and
distribution, and information linkages should be established to ensure the most efficient,
accurate, and cost-effective transmission of information across the supply chain.
Risk-hedging supply chains These are supply chains that utilize strategies aimed at
pooling and sharing resources in a supply chain so that the risks in supply disruption
can be shared. A single entity in a supply chain can be vulnerable to supply disruptions,
but if there is more than one supply source or if alternative supply resources are available, then the risk of disruption is reduced. A company may, for example, increase the
safety stock of its key component to hedge against the risk of supply disruption, and
by sharing the safety stock with other locations that also need this key component, the
cost of maintaining this safety stock can be shared. This type of strategy is common in
retailing, where different retail stores or dealerships share inventory. Information technology is important for the success of these strategies because real-time information on
inventory and demand allows the most cost-effective management and transshipment of
goods between partners sharing the inventory.
Responsive supply chains These are supply chains that utilize strategies aimed at
being responsive and flexible to the changing and diverse needs of the customers. To be
responsive, companies use build-to-order and mass customization processes as a means
to meet the specific requirements of customers.
Agile supply chains These are supply chains that utilize strategies aimed at being
responsive and flexible to customer needs, while the risks of supply shortages or disruptions are hedged by pooling inventory and other capacity resources. These supply
chains essentially have strategies in place that combine the strengths of “hedged” and
“responsive” supply chains. They are agile because they have the ability to be responsive to the changing, diverse, and unpredictable demands of customers on the front end,
while minimizing the back-end risks of supply disruptions.
Demand and supply uncertainty is a good framework for understanding supply chain strategy.
Innovative products with unpredictable demand and an evolving supply process face a major
challenge. Because of shorter and shorter product life cycles, the pressure for dynamically
adjusting and adopting a company’s supply chain strategy is great. In the following section,
we explore the concepts of outsourcing, green sourcing, and total cost of ownership. These
are important tools for coping with demand and supply uncertainty.
407
408
Supply Chain Processes
Section 3
OUTSOURCING
LO 16–2
Explain why companies
outsource processes.
Outsourcing
Moving some of a firm’s
internal activities and
decision responsibility to
outside providers.
Outsourcing is the act of moving some of a firm’s internal activities and decision responsibility to outside providers. The terms of the agreement are established in a contract. Outsourcing goes beyond the more common purchasing and consulting contracts because not only are
the activities transferred, but also resources that make the activities occur, including people,
facilities, equipment, technology, and other assets, are transferred. The responsibilities for
making decisions over certain elements of the activities are transferred as well. Taking complete responsibility for this is a specialty of contract manufacturers such as Flextronics.
The reasons why a company decides to outsource can vary greatly. Exhibit 16.5 lists examples of reasons to outsource and the accompanying benefits. Outsourcing allows a firm to focus
on activities that represent its core competencies. Thus, the company can create a competitive
advantage while reducing cost. An entire function may be outsourced, or some elements of an
activity may be outsourced, with the rest kept in-house. For example, some of the elements of
information technology may be strategic, some may be critical, and some may be performed
less expensively by a third party. Identifying a function as a potential outsourcing target, and
then breaking that function into its components, allows decision makers to determine which
activities are strategic or critical and should remain in-house and which can be outsourced like
commodities. As an example, outsourcing the logistics function will be discussed.
Logis tics Ou t so u rcin g
Logistics
Management functions
that support the complete
cycle of material flow: from
the purchase and internal
control of production
materials; to the planning
and control of work-inprocess; to the purchasing,
shipping, and distribution
of the finished product.
There has been dramatic growth in outsourcing in the logistics area. Logistics is a term that
refers to the management functions that support the complete cycle of material flow: from the
purchase and internal control of production materials; to the planning and control of work-inprocess; to the purchasing, shipping, and distribution of the finished product. The emphasis
on lean inventory means there is less room for error in deliveries. Trucking companies such
as Ryder have started adding the logistics aspect to their businesses—changing from merely
moving goods from point A to point B, to managing all or part of all shipments over a longer
period, typically three years, and replacing the shipper’s employees with their own. Logistics
companies now have complex computer tracking technology that reduces the risk in transportation and allows the logistics company to add more value to the firm than it could if the function were performed in-house. Third-party logistics providers track freight using electronic
data interchange technology and a satellite system to tell customers exactly where its drivers are and when deliveries will be made. Such technology is critical in some environments
where the delivery window may be only 30 minutes long.
exhibit 16.5
Reasons to Outsource and the Resulting Benefits
Financially Driven Reasons
Improve return on assets by reducing inventory and selling unnecessary assets.
Generate cash by selling low-return entities.
Gain access to new markets, particularly in developing countries.
Reduce costs through a lower cost structure.
Turn fixed costs into variable costs.
Improvement-Driven Reasons
Improve quality and productivity.
Shorten cycle time.
Obtain expertise, skills, and technologies that are not otherwise available.
Improve risk management.
Improve credibility and image by associating with superior providers.
Organizationally Driven Reasons
Improve effectiveness by focusing on what the firm does best.
Increase flexibility to meet changing demand for products and services.
Increase product and service value by improving response to customer needs.
Global Sourcing and Procurement
Chapter 16
409
FedEx has one of the most advanced systems available for tracking items being sent
through its services. The system is available to all customers over the Internet. It tells the
exact status of each item currently being carried by the company. Information on the exact
time a package is picked up, when it is transferred between hubs in the company’s network,
and when it is delivered is available on the system. You can access this system at the FedEx
website (www.fedex.com). Select your country on the initial screen and then select “Track
Shipments” in the Track box in the lower part of the page. Of course, you will need the actual
tracking number for an item currently in the system to get information. FedEx has integrated
its tracking system with many of its customers’ in-house information systems.
Another example of innovative outsourcing in logistics involves Hewlett-Packard.
­Hewlett-Packard turned over its inbound raw materials warehousing in Vancouver, British
Columbia, to Roadway Logistics. Roadway’s 140 employees operate the warehouse 24 hours
a day, seven days a week, coordinating the delivery of parts to the warehouse and managing storage. Hewlett-Packard’s 250 employees were transferred to other company activities.
Hewlett-Packard reports savings of 10 percent in warehousing operating costs.
One of the drawbacks to outsourcing is the layoffs that often result. Even in cases where the
outsourcing partner hires former employees, they are often hired back at lower wages with fewer
benefits. Outsourcing is perceived by many unions as an effort to circumvent union contracts.
Fr am e w or k for S upplier Re latio n sh ip s
In theory, outsourcing is a no-brainer. Companies can unload noncore activities, shed balance
sheet assets, and boost their return on capital by using third-party service providers. But in
reality, things are more complicated. It is often difficult to determine what is core and noncore
today, because situations change so quickly today.
Exhibit 16.6 is a useful framework to help managers make appropriate choices for the
structure of supplier relationships. The decision goes beyond the notion that “core competencies” should be maintained under the direct control of management of the firm and that other
activities should be outsourced. In this framework, a continuum that ranges from vertical
integration to arm’s-length relationships forms the basis for the decision.
An activity can be evaluated using the following characteristics: required coordination,
strategic control, and intellectual property. Required coordination refers to how difficult it
is to ensure that the activity will integrate well with the overall process. Uncertain activities
that require much back-and-forth exchange of information should not be outsourced, whereas
activities that are well understood and highly standardized can easily move to business partners who specialize in the activity. Strategic control refers to the degree of loss that would be
incurred if the relationship with the partner were severed. There could be many types of losses
that would be important to consider, including specialized facilities, knowledge of major customer relationships, and investment in research and development. A final consideration is the
potential loss of intellectual property through the partnership.
Intel is an excellent example of a company that recognized the importance of this type of
decision framework in the mid-1980s. During the early 1980s, Intel found itself being squeezed
ex hibit 16.6
KEY IDEA
Companies usually
outsource standard
activities when they are
not part of the “core
competency” of the
firm.
A Framework for Structuring Supplier Relationships
Do not outsource
Outsource
Coordination characteristics
Coordination and interfaces are not well defined.
The information and coordination is specific to
each job.
Technology is immature and there is a need for
“expert” knowledge obtained by experience.
Standardized interfaces, required information is highly codified and standardized
(prices, quantities, delivery schedules, etc.).
Investment is strategic assets
characteristics
Significant investments in highly specialized assets are
needed. The investments cannot be easily recovered
if the relationship terminates. Long-term investments
in specialized R&D, and lengthy learning curves.
Assets are commonly available from a large
number of potential customers or suppliers.
Intellectual property
characteristics
Weak intellectual property protection. Easy-toimitate technology when access is given.
Strong intellectual property protection
Difficult-to-imitate technology
410
Section 3
Supply Chain Processes
out of the market for memory chips (the type it had invented) by Japanese competitors such
as Hitachi, Fujitsu, and NEC. These companies had developed stronger capabilities to develop
and rapidly scale up complex semiconductor manufacturing processes. It was clear by 1985
that a major Intel competency was its ability to design complex integrated circuits—something
it did much better than manufacturing or developing processes for more standardized chips. As
a result, faced with growing financial losses, Intel was forced to exit the memory chip market.
Learning a lesson from the memory market, Intel shifted its focus to the market for microprocessors, which it had invented in the late 1960s. To keep from repeating the mistake with
memory chips, Intel felt it was essential to develop strong capabilities in process development and manufacturing. A pure “core competency” strategy would have suggested that Intel
focus on the design of microprocessors and use outside partners to manufacture them. Given
the close connection between semiconductor product development and process development,
OSCM AT WORK
Capability Sourcing at 7-Eleven
The term capability sourcing was coined to refer to the way
companies focus on the things they do best and outsource
other functions to key partners. The idea is that owning
capabilities may not be as important as having control of
those capabilities. This allows many additional capabilities
to be outsourced. Companies are under intense pressure to
improve revenue and margins because of increased competition. An area where this has been particularly intense is the
convenience store industry, where 7-Eleven is a major player.
Before 1991, 7-Eleven was one of the most vertically
integrated convenience store chains. When it is vertically
integrated, a firm controls most of the activities in its supply
chain. In the case of 7-Eleven, the firm owned its own distribution network, which delivered gasoline to each store,
made its own candy and ice, and required the managers
to handle store maintenance, credit card processing, store
payroll, and even the in-store information technology (IT)
system. For a while, 7-Eleven even owned the cows that
produced the milk sold in the stores. But it was difficult for
7-Eleven to manage costs in this diverse set of functions.
At that time, 7-Eleven had a Japanese branch that was
very successful but was based on a totally different integration model. Rather than using a company-owned and
vertically integrated model, the Japanese stores had partnerships with suppliers that carried out many of the dayto-day functions. Those suppliers specialized in each area,
enhancing quality and improving service while reducing
cost. The Japanese model involved outsourcing everything
possible without jeopardizing the business by giving competitors critical information. A simple rule said that if a partner could provide a capability more effectively than 7-Eleven
could itself, that capability should be outsourced. In the
United States, the company eventually outsourced activities
such as human resources, finance, information technology,
logistics, distribution, product development, and packaging.
7-Eleven still maintains control of all vital information and
handles all merchandising, pricing, positioning, promotion
of gasoline, and ready-to-eat food.
The following chart shows how 7-Eleven has structured
key partnerships.
Activity
Outsourcing Strategy
Gasoline
Outsourced distribution to Citgo. Maintains control over pricing and promotion. These are activities that
can differentiate its stores.
Snack foods
Frito-Lay distributes its products directly to the stores. 7-Eleven makes critical decisions about order
quantities and shelf placement. 7-Eleven mines extensive data on local customer purchase patterns to
make these decisions at each store.
Prepared foods
Joint venture with E. A. Sween: Combined Distribution Centers (CDCs), a direct-store delivery operation
that supplies 7-Eleven stores with sandwiches and other fresh goods two times a day
Specialty products
Many are developed specially for 7-Eleven customers. For example, 7-Eleven worked with Hershey to
develop an edible straw used with the popular Twizzler treat. Worked with Anheuser-Busch on special
NASCAR and Major League Baseball promotions.
Data analysis
7-Eleven relies on an outside vendor, IRI, to maintain and format purchasing data while keeping the data
proprietary. Only 7-Eleven can see the actual mix of products its customers purchase at each location.
New capabilities
American Express supplies automated teller machines.
Western Union handles money wire transfers.
CashWorks furnishes check-cashing capabilities.
Electronic Data Systems (EDS) maintains network functions.
Global Sourcing and Procurement
Chapter 16
however, relying on outside parties for manufacturing would likely have created costs in terms
of longer development lead times. Over the late-1980s, Intel invested heavily in building
world-class capabilities in process development and manufacturing. These capabilities are
one of the chief reasons it has been able to maintain approximately 90 percent of the personal
computer microprocessor market, despite the ability of competitors like AMD to “clone” Intel
designs relatively quickly. Expanding its capabilities beyond its original core capability of
product design has been a critical ingredient in Intel’s sustained success.
Good advice is to keep control of—or acquire—activities that are true competitive differentiators or have the potential to yield a competitive advantage, and to outsource the rest.
It is important to make a distinction between “core” and “strategic” activities. Core activities
are key to the business, but do not confer a competitive advantage, such as a bank’s information technology operations. Strategic activities are a key source of competitive advantage.
Because the competitive environment can change rapidly, companies need to monitor the situation constantly, and adjust accordingly. As an example, Coca-Cola, which decided to stay out
of the bottling business in the early 1900s, partnered instead with independent bottlers and
quickly built market share. The company reversed itself in the 1980s when bottling became a
key competitive element in the industry.
G r e e n S our cing
Being environmentally responsible has become a business imperative, and many firms are
looking to their supply chains to deliver “green” results. A significant area of focus relates to
how a firm works with suppliers where the opportunity to save money and benefit the environment might not be a strict trade-off proposition. Financial results can often be improved
through both cost reductions and boosting revenues.
Green sourcing is not just about finding new environmentally friendly technologies or
increasing the use of recyclable materials. It can also help drive cost reductions in a variety of
ways, including product content substitution, waste reduction, and lower usage.
A comprehensive green sourcing effort should assess how a company uses items that are purchased internally, in its own operations, or in its products and services. As costs of commodity
items like steel, electricity, and fossil fuels continue to increase, properly designed green sourcing efforts should find ways to significantly reduce and possibly eliminate the need for these
types of commodities. As an example, consider retrofitting internal lighting in a large office
building to a modern energy-efficient technology. Electricity cost savings of 10 to 12 percent
per square foot can easily translate into millions of dollars in associated electricity cost savings.
Another important cost area in green sourcing is waste reduction opportunities. This
includes everything from energy and water to packaging and transportation. A great example
of this is the redesigned milk jug introduced recently by leading grocery retailers. Using the
new jug, with more rectangular dimensions and a square base, cuts the associated water consumption of the jugs by 60 to 70 percent compared to earlier jug designs because the new
design does not require the use of milk crates. Milk crates
typically become filthy during use due to spillage and other
natural factors; thus, they are usually hosed down before
reuse, consuming thousands of gallons of water. The new
design also reduces fuel costs. Since crates are no longer
used, they also do not have to be transported back to the
dairy plant or farm distribution point for future shipments.
Furthermore, the new jugs have the unexpected benefit
of fitting better in modern home refrigerator doors and
allow retailers to fit more of them in their in-store coolers.
Breakthrough results like the new milk jug can result from
comprehensive partnerships between users and their suppliers working to find innovative solutions.
Many companies have found that working with suppliers can result in opportunities that improve revenue. The
opportunity to turn waste products into sources of revenue © Kevin Clifford/AP Images
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Section 3
might be significant. For example, a leading beverage manufacturer operates a recycling subsidiary that sources used aluminum cans from a large number of suppliers. The subsidiary
actually processes more aluminum cans than are used in the company’s own products, consequently developing a strong secondary revenue stream for the company.
In other cases, green sourcing can help establish entirely new lines of business to serve
environmentally conscious customers. In the cleaning products aisle of a supermarket, shoppers will find numerous options of “green” cleaning products from a variety of consumer
products companies. These products typically use natural ingredients in lieu of chemicals, and
many are in concentrated amounts to reduce overall packaging costs.
Logistics suppliers could find business opportunities coming directly to them as a result of the
green trend. A large automobile manufacturer completed a project to “green” its logistics/distribution network. The automaker analyzed the shipping carriers, locations, and overall efficiency
of its distribution network for both parts and finished automobiles. By increasing the use of rail
transportation for parts, consolidating shipments in fewer ports, and partnering with its logistics
providers to increase fuel efficiency for both marine and road transportation, the company reduced
its overall distribution-related carbon dioxide emissions by several thousand tons per year.
The following is an outline of a six-step process (see Exhibit 16.7) designed to transform a
traditional process to a green sourcing process.
1.
Assess the opportunity. For a given category of expense, all relevant costs need to
be taken into account. The five most common areas include electricity and other energy
costs; disposal and recycling; packaging; commodity substitution (alternative materials
to replace materials such as steel or plastic); and water (or other related resources). These
costs are identified and incorporated into an analysis of total cost (sometimes referred
to as “spend” cost analysis) at this step. From this analysis, it is possible to prioritize the
different costs based on the highest potential savings and criticality to the organization.
This is important in directing effort to where it will likely have the most
impact on the firm’s financial position and cost reduction goals.
2. Engage internal supply chain sourcing agents. Internal sourcing agents are those within the firm that purchase items and have
direct knowledge of business requirements, product specifications,
and other internal perspectives inherent in the supply chain. These
individuals and groups need to be “on-board” and be partners in the
improvement process to help set realistic green goals. The goal of
generating no waste, for example, becomes a cross-functional supply chain effort that relies heavily on finding and developing the
right suppliers. These internal managers need to identify the most
significant opportunities. They can develop a robust baseline model
of what should be possible for reducing current and ongoing costs.
In the case of procuring new equipment, for example, the baseline
model would include not just the initial price of the equipment as in
traditional sourcing, but also energy, disposal, recycling, and maintenance costs.
3. Assess the supply base. A sustainable sourcing process requires
engaging new and existing vendors. As in traditional sourcing, the
firm needs to understand vendor capabilities, constraints, and product offering. The green process needs to be augmented with formal
requirements that relate to green opportunities, including possible
commodity substitutions and new manufacturing processes. These
requirements need to be incorporated in vendor bid documents or the
Fly ash is generally stored at coal power
request for proposals (RFPs).
plants or placed in landfills as shown here.
A good example is concrete that uses fly ash, a by-product from
About 43 percent is recycled, reducing the
coal-fired
power plants. Fly ash can be substituted for Portland
harmful impact on the environment from
cement in ready-mix concrete or in concrete blocks to produce a
landfills.
© Carolyn Kaster/AP Images
stronger and lighter product with reduced water consumption. Fly
Global Sourcing and Procurement
ex hibit 16.7
Chapter 16
Six-Step Process for Green Sourcing
1. Assess the
opportunity
2. Engage
sourcing agents
3. Assess the
supply base
— Evaluate and
prioritize costs
— Cross-functional
ownership of the
process
— Engage vendors
in the process
6. Institutionalize the
sourcing strategy
5. Implement
sourcing strategy
4. Develop the
sourcing strategy
— Metrics and audits
to monitor
performance
— Select vendors and
products based on
criteria
— Develop
quantitative criteria
ash substitution helped a company reduce its exposure to volatile and rapidly increasing prices for cement. At the same time, the reduced weight of the block lowered
transportation costs to the company’s new facilities. The company was also able to
establish a specification incorporating fly ash for all new construction sites to follow.
Finally, the substitution also helped the power plant by providing a new market for
the fly ash, which previously had to be discarded.
4. Develop the sourcing strategy. The main goal with this step is to develop quantitative and qualitative criteria that will be used to evaluate the sourcing process. These
are needed to properly analyze associated costs and benefits. These criteria need to
be clearly articulated in bid documents and RFPs when working with potential suppliers so that their proposals will address relevant goals related to sustainability.
5. Implement the sourcing strategy. The evaluation criteria developed in step 4
should help in the selection of vendors and products for each business requirement.
The evaluation process should consider initial cost and the total cost of ownership for the items in the bid. So, for example, energy-efficient equipment that is
proposed with a higher initial cost may, over its productive life, actually result in a
lower total cost due to energy savings and a related lower carbon footprint. Relevant
green opportunities such as energy efficiency and waste reduction need to be modeled and then incorporated into the sourcing analysis to make it as comprehensive
as possible and to facilitate an effective vendor selection process that supports the
firm’s needs.
6. Institutionalize the sourcing strategy. Once the vendor is selected and contracts
finalized, the procurement process begins. Here, the sourcing and procurement
department needs to define a set of metrics against which the supplier will be measured for the contract’s duration. These metrics should be based on performance,
delivery, compliance with pricing guidelines, and similar factors. It is vital that metrics that relate to the company’s sustainability goals are considered as well. Periodic
audits may also need to be incorporated in the process to directly observe practices
that relate to these metrics to ensure honest reporting of data.
A key aspect of green sourcing, compared to a traditional process, is the expanded
view of the sourcing decision. This expanded view requires the incorporation of new
criteria for evaluating alternatives. Further, it requires a wider range of internal integration such as designers, engineers, and marketers. Finally, visualizing and capturing the green sourcing savings often involve greater complexity and longer payback
periods compared to a traditional process.
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TOTAL COST OF OWNERSHIP
LO 16–3
Analyze the total cost of
ownership.
Total cost of ownership
Estimate of the cost of
an item that includes all
the costs related to the
procurement and use
of the item, including
disposing of the item after
its useful life.
The total cost of ownership (TCO) is an estimate of the cost of an item that includes all the costs
related to its procurement and use, including any related costs in disposing of the item after it is
no longer useful. The concept can be applied to a company’s internal costs or it can be viewed
more broadly to consider costs throughout the supply chain. To fully appreciate the cost of purchasing an item from a particular vendor, an approach that captures the costs of the activities
associated with purchasing and actually using the item should be considered. Depending on the
complexity of the purchasing process, activities such as prebid conferences, visits by potential
suppliers, and even visits to potential suppliers can significantly impact the total cost of the item.
A TCO analysis is highly dependent on the actual situation; in general, though, the costs outlined in Exhibit 16.8 should be considered. The costs can be categorized into three broad areas:
acquisition costs, ownership costs, and post-ownership costs. Acquisition costs are the initial costs
associated with the purchase of materials, products, and services. They are not long-term costs
of ownership but represent an immediate cash outflow. Acquisition costs include the prepurchase
costs associated with preparing documents to distribute to potential suppliers, identifying suppliers and evaluating suppliers, and other costs associated with actually procuring the item. The
actual purchase prices, including taxes, tarriffs, and transportation costs, are also included.
Ownership costs are incurred after the initial purchase and are associated with the ongoing use
of the product or material. Examples of costs that are quantifiable include energy usage, scheduled
maintenance, repair, and financing (leasing situation). There can also be qualitative costs such as
aesthetic factors (e.g., the item is pleasing to the eye), and ergonomic factors (e.g., productivity
improvement or reducing fatigue). These ownership costs can often exceed the initial purchase
price and have an impact on cash flow, profitability, and even employee morale and productivity.
exhibit 16.8
Total Cost of Ownership
Acquisition costs
· Purchase planning costs
· Quality costs
· Taxes
· Purchase price
· Financing costs
Total cost of ownership
Ownership costs
· Energy costs
· Maintenance and repair
· Financing
· Supply chain/supply
network costs
Post-ownership costs
· Disposal
· Environmental costs
· Warranty costs
· Product liability costs
· Customer dissatisfaction costs
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Major costs associated with post-ownership include salvage value and disposal costs. For
many purchases, there are established markets that provide data to help estimate reasonable
future values, such as the Kelley Blue Book for used automobiles. Other areas that can be
included are the long-term environmental impact (particularly when the firm has sustainability goals), warranty and product liabilities, and the negative marketing impact of low customer satisfaction with the item.
Overemphasis on acquisition cost or purchase price frequently results in a failure to address
other significant ownership and post-ownership costs. TCO is a philosophy for understanding
all relevant costs of doing business with a particular supplier for a good or service. It is not only
relevant for a business that wants to reduce its cost of doing business but also for a firm that
aims to design products or services that provide the lowest total cost of ownership to customers. For example, some automobile manufacturers have extended the tune-up interval on many
models to 100,000 miles, thereby reducing vehicle operating cost for car owners. Viewing TCO
in this way can lead to an increased value of the product to existing and potential customers.
These costs can be estimated as cash inflows (the sale of used equipment, etc.) or outflows
(such as purchase prices, demolition of an obsolete facility, etc.). The following example
shows how this analysis can be organized using a spreadsheet. Keep in mind that the costs
considered need to be adapted to the decision being made. Costs that do not vary based on the
decision need not be considered, but relevant costs that vary depending on the decision should
be included in the analysis.
TCO actually draws on many areas for a thorough analysis. These include finance (net
present value), accounting (product pricing and costing), operations management (reliability,
quality, need, and inventory planning), marketing (demand), and information technology (systems integration). It is probably best to approach this using a cross-functional team representing the key functional areas.
EXAMPLE 16.1: Total Cost of Ownership Analysis
Consider the analysis of the purchase of a copy machine that might be used in a copy center.
The machine has an initial cost of $120,000 and is expected to generate income of $40,000 per
year. Supplies are expected to be $7,000 per year and the machine needs to be overhauled during year 3 at a cost of $9,000. It has a salvage value of $7,500 when we plan to sell it at year 6.
SOLUTION
Laying these costs out over time can lead to the use of net present value analysis to evaluate
the decision. Consider Exhibit 16.9, where the present values of each yearly stream are discounted to now. (See Appendix E for a present value table.) As we can see, the present value
in this analysis shows that the present value cost of the copier is $12,955.
ex hibit 16.9
Analysis of the Purchase of an Office Copier
Year
Now
1
2
3
4
5
6
Cash inflows from using the machine
$ 40,000
$ 40,000
$ 40,000
$ 40,000
$ 40,000
$ 40,000
Supplies needed to use the machine
−$7,000
−$7,000
−$7,000
−$7,000
−$7,000
−$7,000
−$120,000
Initial Investment
−$9,000
Manufacturer required overhaul
Salvage value
$ 7,500
−$120,000
Total of annual streams
Discount factor from Appendix C 1/(1 + .2)
Year
Present value − yearly
Present value
$ 33,000
$ 33,000
$ 24,000
$ 33,000
$ 33,000
$ 40,500
1.000
0.833
0.694
0.579
0.482
0.402
0.335
−$120,000
$ 27,500
$ 22,917
$ 13,889
$ 15,914
$ 13,262
$ 13,563
−$12,955
Discount factor = 20%.
Note: These calculations were done using the full precision of a spreadsheet.
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Supply Chain Processes
It is important that any analysis is adapted to the particular scenario. Such factors as
exchange rates, the risk of doing business in a particular region of the world, transportation,
and other items are often important. Depending on the alternatives, there are a host of factors,
often going beyond cost, that need to be considered. Adapting this type of cost analysis and
combining it with a more qualitative risk analysis are useful in actual company situations.
MEASURING SOURCING PERFORMANCE
LO 16–4
Evaluate sourcing
performance
Inventory turnover
A measure of supply chain
efficiency.
Cost of goods sold
The annual cost for a
company to produce the
goods or services provided
to customers.
Average aggregate
inventory value
The average total value of
all items held in inventory
for the firm, valued at cost.
exhibit 16.10
One view of sourcing is centered on the inventories that are positioned in the system.
Exhibit 16.10 shows how hamburger meat and potatoes are stored in various locations in
a typical fast-food restaurant chain. Here we see the steps that the beef and potatoes move
through on their way to the local retail store and then to the customer. Inventory is carried at
each step, and this inventory has a particular cost to the company. Inventory serves as a buffer,
thus allowing each stage to operate independently of the others. For example, the distribution
center inventory allows the system that supplies the retail stores to operate independently of
the meat and potato packing operations. Because the inventory at each stage ties up money, it
is important that the operations at each stage are synchronized to minimize the size of these
buffer inventories. The efficiency of the supply chain can be measured based on the size of the
inventory investment in the supply chain. The inventory investment is measured relative to the
total cost of the goods that are provided through the supply chain.
Two common measures to evaluate supply chain efficiency are inventory turnover and
weeks of supply. These essentially measure the same thing. Weeks of supply is the inverse of
inventory turnover times 52. Inventory turnover is calculated as follows:
Cost of goods sold
_____________________________
Inventory turnover =
​​      ​​
Average aggregate inventory value
The cost of goods sold is the annual cost for a company to produce the goods or services
provided to customers; it is sometimes referred to as the cost of revenue. This does not include
the selling and administrative expenses of the company. The average aggregate inventory
value is the average total value of all items held in inventory for the firm valued at cost. It
includes the raw material, work-in-process, finished goods, and distribution inventory considered owned by the company.
Inventory in the Supply Chain—Fast-Food Restaurant
Potatoes—
30 /lb.
Potatoes—
25 /lb.
Potato
farm
Bags of frozen
French fries—
35 /lb.
Beef patties—$1.00/lb.
Frozen french
fries—40 /lb.
Potato processing and packing
Distribution
center
Cattle
farm
Slaughter
house
Cows—
50 /lb.
​[​16.1​]​
Beef
carcasses—
55 /lb.
Retail
store
Customer
Meat
packing
Beef loins—
60 /lb.
Frozen beef
patties—
65 /lb.
Hamburgers—
$8.00/lb.
French fries—
$3.75/lb.
Global Sourcing and Procurement
Chapter 16
Good inventory turnover values vary by industry and the type of products being handled.
At one extreme, a grocery store chain may turn inventory over 100 times per year. Values of
six to seven are typical for manufacturing firms.
In many situations, particularly when distribution inventory is dominant, weeks of supply
is the preferred measure. This is a measure of how many weeks’ worth of inventory is in the
system at a particular point in time. The calculation is as follows:
⎛ Average aggregate inventory value ⎞
Weeks of supply = ​​ ____________________________
​
​
​​ × 52 weeks
⎝
⎠
Cost of goods sold
⎜
⎟
​[​16.2​]​
When company financial reports cite inventory turnover and weeks of supply, we can
assume that the measures are being calculated firmwide. We show an example of this type
of calculation in the example that follows using Dell Computer data. These calculations,
though, can be done for individual entities within the organization. For example, we might
be interested in the production raw materials inventory turnover or the weeks of supply
associated with the warehousing operation of a firm. In these cases, the cost would be that
associated with the total amount of inventory that runs through the specific inventory. In
some very-low-inventory operations, days or even hours are a better unit of time for measuring supply.
A firm considers inventory an investment because the intent is for it to be used in the
future. Inventory ties up funds that could be used for other purposes, and a firm may have
to borrow money to finance the inventory investment. The objective is to have the proper
amount of inventory and to have it in the correct locations in the supply chain. Determining
the correct amount of inventory to have in each position requires a thorough analysis of the
supply chain coupled with the competitive priorities that define the market for the company’s
products.
EXAMPLE 16.2: Inventory Turnover Calculation
Dell Computer reported the following information in a recent annual report (all dollar amounts
are expressed in millions):
Net revenue
$49,205
Cost of revenue
$40,190
Production materials on hand
$228
Work-in-process and finished goods on hand
$231
Days of supply in inventory
4 days
The cost of revenue corresponds to what we call cost of goods sold. One might think that U.S.
companies, at least, would use a common accounting terminology, but this is not true. The
inventory turnover calculation is
40,190
​Inventory turnover = _______
​
​= 87.56 turns per year​
228 + 231
This is amazing performance for a high-tech company, but it explains much of why the company is such a financial success.
The corresponding weeks of supply calculation is
⎛ 228 + 231 ⎞
​Weeks of supply = ​ ​_
​
​ ​× 52 = .59 week​
⎝ 40, 190 ⎠
⎜
⎟
417
Weeks of supply
Preferred measure of
supply chain efficiency
that is mathematically
the inverse of inventory
turnover times 52.
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Supply Chain Processes
Concept Connections
LO 16–1 Explain what strategic sourcing is.
Summary
∙ Sourcing is a term that captures the strategic nature
of purchasing in today’s global and Internet-connected
marketplace.
∙ The sourcing/purchasing design matrix captures the
scope of the topic that ranges from one-time spot purchases, to a complex strategic alliance arrangement
with another firm.
∙ A phenomenon known as the bullwhip effect has been
observed in many industries. This is when changes
in demand are magnified as they move from the customer to the manufacturer. The phenomenon is caused
by long lead times and the fact that there are often
multiple stages in a supply chain.
∙ Supply chains can be categorized based on demand
and supply uncertainty characteristics. Four types of
supply chains are identified: (1) efficient, (2) riskhedging, (3) responsive, and (4) agile.
Key Terms
Strategic sourcing The development and management
of supplier relationships to acquire goods and services in
a way that aids in achieving the needs of a business.
Sourcing A process suitable for procuring products that
are strategically important to the firm.
Specificity Refers to how commonly available the material is and whether substitutes can be used.
Request for proposal (RFP) A solicitation that asks for a
detailed proposal from a vendor interested in supplying
an item.
Vendor managed inventory When a customer allows
the supplier to manage the inventory policy of an item or
group of items.
Forward buying A term that refers to when a customer,
responding to a promotion, buys far in advance of when
an item will be used.
Bullwhip effect The variability in demand is magnified
as we move from the customer to the producer in the
supply chain.
Continuous replenishment A program for automatically
supplying groups of items to a customer on a regular
basis.
Functional products Staples that people buy in a wide
range of retail outlets, such as grocery stores and gas
stations.
Innovative products Products such as fashionable
clothes and personal computers that typically have a life
cycle of just a few months.
Stable supply process A process where the underlying
technology is stable.
Evolving supply process A process where the underlying technology changes rapidly.
LO 16–2 Explain why companies outsource processes.
Summary
∙ Outsourcing is when a firm contracts with an outside
provider for activities essential to the firm’s success.
∙ The transportation of a firm’s products (referred to as
logistics) is often outsourced.
∙ Whether an activity is outsourced or not often depends
on criteria related to (1) coordination requirements,
(2) strategic control, and (3) intellectual property
issues.
∙ Green sourcing has become an imperative for many
firms and it may create new markets for a firm’s
products.
Key Terms
Outsourcing Moving some of a firm’s internal activities
and decision responsibility to outside providers.
Logistics Management functions that support the complete cycle of material flow: from the purchase and
internal control of production materials; to the planning
and control of work-in-process; to the purchasing, shipping, and distribution of the finished product.
Global Sourcing and Procurement
Chapter 16
419
LO 16–3 Analyze the total cost of ownership.
Summary
∙ This is an approach to understanding the total cost of
an item.
∙ Costs can generally be categorized into three areas:
(1) acquisition costs, (2) ownership costs, and (3)
post-ownership costs.
Key Terms
Total cost of ownership Estimate of the cost of an item
that includes all the costs related to the procurement and
use of the item, including disposing of the item after its
useful life.
LO 16–4 Evaluate sourcing performance.
Summary
∙ Inventory turn and weeks of supply are the most common measures to evaluate supply chain efficiency.
These measures can vary greatly depending on the
industry.
Key Terms
Inventory turnover A measure of supply chain
efficiency.
Cost of goods sold The annual cost for a company to
produce the goods or services provided to customers.
Average aggregate inventory value The average total value
of all items held in inventory for the firm, valued at cost.
Weeks of supply Preferred measure of supply chain
efficiency that is mathematically the inverse of inventory
turnover times 52.
​[​16.1​]​
Cost of goods sold
Inventory turnover = _____________________________
​​     ​​
Average aggregate inventory value
​​[​​16.2​]​​​
⎛ Average aggregate inventory value ⎞
Weeks of supply = ​​ ____________________________
​
​
​​ × 52 weeks
⎝
⎠
Cost of goods sold
⎜
⎟
Discussion Questions
1. What recent changes have caused supply chain management to gain importance?
2. Describe the differences between functional and innovative products.
3. What are characteristics of efficient, responsive, risk-hedging, and agile supply chains?
Can a supply chain be both efficient and responsive? Risk-hedging and agile? Why or
why not?
4. With so much productive capacity and room for expansion in the United States, why
would a company based in the United States choose to purchase items from a foreign
firm? Discuss the pros and cons.
5. As a supplier, which factors about a buyer (your potential customer) would you consider
to be important in setting up a long-term relationship?
6. Describe how outsourcing works. Why would a firm want to outsource?
7. Have you ever purchased a product based on purchase price alone and were surprised
by the eventual total cost of ownership (TCO), either in money or in time? Describe the
situation.
8. Why might managers resist buying a more expensive piece of equipment, known to have
a lower TCO, than a less expensive item?
LO 16–1
LO 16–2
LO 16–3
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Section 3
LO 16–4
9. Why is it desirable to increase a company’s inventory turnover ratio?
10. Research and compare the inventory turnover ratios of three large retailers: Walmart, Target, and Nordstrom. Use the same financial Website for all three, and compare numbers
from the same time frame. What do these ratios tell you? Are you surprised by what you
found?
Objective Questions
LO 16–1
LO 16–2
LO 16–3
1. What term refers to the development and management of supplier relationships in order
to acquire goods and services in a way that helps achieve the immediate needs of a
business?
2. Sometimes a company may need to purchase goods or services that are unique, very complex, and/or extremely expensive. These would not be routine purchases, but there may
be a number of vendors that could supply what is needed. What process would be used to
transmit the company’s needs to the available vendors, asking for a detailed response to
the needs?
3. Sony Electronics produces a wide variety of electronic products for the consumer marketplace, such as laptop computers, PlayStation game consoles, and tablet computers. What
type of products would these be considered in the Supply Chain Uncertainty Framework?
4. One product that Staples sells a lot of is copy paper. According to the Supply Chain
Uncertainty Framework, what supply chain strategy is appropriate for this product?
5. What is the term used for the act of moving some of a company’s internal activities and
decision-making processes to outside providers?
6. What is the term used for a company moving management of the complete cycle of material flow to an outside provider?
7. Many bottled water manufacturers have recently worked with their suppliers to switch
over to bottles using much less plastic than before, reducing the amount of plastic that
needs to be transported, recycled, and/or disposed of. What sourcing practice is this an
example of?
8. What term is used to refer to those activities that are the key source of competitive
advantage?
9. What three main categories of costs are considered in figuring the total cost of ownership?
10. Which category of lifetime product costs are sometimes overemphasized, leading to a
failure to fully recognize the total cost of ownership?
11. One of your Taiwanese suppliers has bid on a new line of molded plastic parts that is
currently being assembled at your plant. The supplier has bid $0.10 per part, given a
forecast you provided of 200,000 parts in year 1; 300,000 in year 2; and 500,000 in year
3. Shipping and handling of parts from the supplier’s factory is estimated at $0.01 per
unit. Additional inventory handling charges should amount to $0.005 per unit. Finally,
administrative costs are estimated at $20 per month.
Although your plant is able to continue producing the part, the plant would need to
invest in another molding machine, which would cost $10,000. Direct materials can be
purchased for $0.05 per unit. Direct labor is estimated at $0.03 per unit plus a 50 percent
surcharge for benefits; indirect labor is estimated at $0.011 per unit plus 50 percent benefits. Up-front engineering and design costs will amount to $30,000. Finally, management has insisted that overhead be allocated if the parts are made in-house at a rate of
100 percent of direct labor cost. The firm uses a cost of capital of 15 percent per year.
What should you do, continue to produce in-house or accept the bid from your Taiwanese supplier? (Answer in Appendix D)
12. Your company assembles five different models of a motor scooter that is sold in specialty
stores in the United States. The company uses the same engine for all five models. You
have been given the assignment of choosing a supplier for these engines for the coming
year. Due to the size of your warehouse and other administrative restrictions, you must
order the engines in lot sizes of 1,000 each. Because of the unique characteristics of the
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engine, special tooling is needed during the manufacturing process for which you agree
to reimburse the supplier. Your assistant has obtained quotes from two reliable engine
suppliers and you need to decide which to use. The following data have been collected.
Requirements (annual forecast)
12,000 units
Weight per engine
22 pounds
Order processing cost
$125 per order
Inventory carry cost
20 percent of the average value of inventory per year
Note: Assume that half of the lot size is in inventory, on average (1,000/2 = 500 units).
Two qualified suppliers have submitted the following quotations.
Supplier 1
Unit Price
Supplier 2
Unit Price
$510.00
$505.00
1,500 to 2,999 units/order
500.00
$505.00
3,000+ units/order
490.00
488.00
Order Quantity
1 to 1,499 units/order
Tooling costs
$22,000
$20,000
Distance
125 miles
100 miles
Your assistant has obtained the following freight rates from your carrier.
Truckload (40,000 lb. each load):
$0.80 per ton-mile
Less-than-truckload:
$1.20 per ton-mile
Note: Per ton-mile = 2,000 lb. per mile
a. Perform a total cost of ownership analysis and select a supplier.
b. Would it make economic sense to order in truckload quantities? Would your supplier
selection change if you ordered truckload quantities?
13. Which supply chain efficiency measure is more appropriate when the majority of inventory is held in distribution channels?
14. What do you call the average total value of all items held in inventory for a firm, at cost?
15. The owner of a large machine shop has just finished its financial analysis from the prior
fiscal year. Following is an excerpt from the final report:
Net revenue
Cost of goods sold
$375,000
322,000
Value of production materials on-hand
42,500
Value of work-in-process inventory
37,000
Value of finished goods on-hand
12,500
a. Compute the inventory turnover ratio (ITR).
b. Compute the weeks of supply (WS).
16. The McDonald’s fast-food restaurant on campus sells an average of 4,000 quarter-pound
hamburgers each week. Hamburger patties are resupplied twice a week, and on average
the store has 350 pounds of hamburger in stock. Assume that the hamburger patties cost
$1.00 a pound. What is the inventory turnover for the hamburger patties? On average,
how many days of supply are on-hand? (Answer in Appendix D)
17. U.S. Airfilter has hired you as a supply chain consultant. The company makes air filters for residential heating and air-conditioning systems. These filters are made in a single plant located in Louisville, Kentucky, in the United States. They are distributed to
LO 16–4
421
422
Section 3
Supply Chain Processes
retailers through wholesale centers in 100 locations in the United States, Canada, and
Europe. You have collected the following data relating to the value of inventory in the
U.S. Airfilter supply chain.
Quarter 1
(January
through March)
Quarter 2
(April
through June)
Quarter 3
(July through
September)
Quarter 4
(October through
December)
300
75
30
350
60
33
405
75
20
375
70
15
280
295
340
350
50
40
55
60
100
105
120
150
25
10
5
27
11
4
23
15
5
30
16
5
Sales (total quarter):
United States
Canada
Europe
Cost of goods sold
(total quarter)
Raw materials at
the Louisville
plant (end-of-quarter)
Work-in-process
and finished
goods at the
Louisville plant
(end-of-quarter)
Distribution center
Inventory (end-of-quarter):
United States
Canada
Europe
All amounts in millions of U.S. dollars.
a. What is the average inventory turnover for the firm?
b. If you were given the assignment to increase inventory turnover, what would you
focus on? Why?
c. The company reported that it used $500M worth of raw material during the year. On
average, how many weeks of supply of raw material are on-hand at the factory?
Analytics Exercise: Global Sourcing Decisions—Grainger: Reengineering the
China/U.S. Supply Chain
W. W. Grainger, Inc., is a leading supplier of maintenance, repair, and operating (MRO) products to businesses and institutions in the United States, Canada, and
Mexico, with an expanding presence in Japan, India,
China, and Panama. The company works with more
than 3,000 suppliers and runs an extensive Website
(www.grainger.com), where it offers nearly 900,000
products. The products range from industrial adhesives
used in manufacturing, to hand tools, janitorial supplies,
lighting equipment, and power tools. When something
is needed by one of its 1.8 million customers, it is often
needed quickly, so quick service and product availability
are key drivers to Grainger’s success.
Your assignment involves studying a specific part of
Grainger’s supply chain. Grainger works with over 250
suppliers in the China and Taiwan region. These suppliers produce products to Grainger’s specifications and
ship to the United States using ocean freight carriers
from four major ports in China and Taiwan. From these
ports, product is shipped to U.S. entry ports in either
Seattle, Washington, or Los Angeles, California. After
passing through customs, the 20- and 40-foot containers
are shipped by rail to Grainger’s central distribution center in Kansas City, Kansas. The containers are unloaded
and quality is checked in Kansas City. From there, individual items are sent to regional warehouses in nine U.S.
locations, a Canadian site, and Mexico.
The Current China/Taiwan Logistics
Arrangement
The contracts that Grainger has with Chinese and Taiwanese suppliers currently specify that the supplier owns
the product and is responsible for all costs incurred until
the product is delivered to the shipping port. These are
commonly referred to as free on board (FOB) shipping
port contracts. Grainger works with a freight forwarding company that coordinates all shipments from the
Asian suppliers.
Global Sourcing and Procurement
© Debbie Noda/Modesto Bee/ZUMAPRESS/Alamy
Currently, suppliers have the option of either shipping product on pallets to consolidation centers at the
port locations or packing the product in 20- and 40-foot
containers that are loaded directly on the ships bound
for the United States. In many cases, the volume from a
supplier is relatively small and will not sufficiently fill
a container. The consolidation centers are where individual pallets are loaded into the containers that protect
the product while being shipped across the Pacific Ocean
and then to Grainger’s Kansas City distribution center.
The freight forwarding company coordinates the efficient
shipping of the 20- and 40-foot containers. These are
the same containers that are loaded onto rail cars in the
United States.
Currently, about 190,000 cubic meters of material
are shipped annually from China and Taiwan. This is
expected to grow about 15 percent per year over the next
five years. About 89 percent of all the volume shipped
from China and Taiwan are sent directly from the suppliers in 20- and 40-foot containers that are packed by the
supplier at the supplier site. Approximately 21 percent
are packed in the 20-foot containers and 79 percent in
40-foot containers. The 20-foot containers can hold 34
cubic meters (CBM) of material, and the 40-foot containers, 67 CBM. The cost to ship a 20-foot container is $480,
and for a 40-foot container, $600; this is from any port
location in China or Taiwan and to either Los Angeles
or Seattle. Grainger estimates that these supplier-filled
containers average 85 percent full when they are shipped.
The remaining 11 percent shipped from China and
Taiwan go through consolidation centers that are located
at each port. These consolidation centers are run by the
freight forwarding company and cost about $75,000 per
year each to operate. At the volumes that are currently
running through these centers, the variable cost is $4.90
per CBM. The variable cost of running a consolidation
center could be reduced to about $1.40 per CBM using
technology if the volume could be increased to at least
50,000 CBM per year. Now there is much variability in
Chapter 16
423
the volume run at each center and it only averages about
5,000 CBM per site.
Material at the consolidation centers is accumulated
on an ongoing basis, and as containers are filled they are
sent to the port. Volume is sufficient enough that at least
one 40-foot container is shipped from each consolidation
center each week. Grainger has found that the consolidation centers can load all material into 40-foot containers
and utilize 96 percent of the capacity of the container.
Grainger ships from four major port locations.
Approximately 10 percent of the volume is shipped from
the north China port of Qingdao, while 42 percent is
shipped from the central China port of Shanghai/Ningbo.
Another 10 percent is shipped from Kaohsiung in ­Taiwan.
The final 38 percent is shipped from the southern Yantian/Hong Kong port. Consolidation centers are currently
run in each location.
Grainger management feels that it may be possible to
make this part of its supply chain more efficient.
Specific questions to address in your
analysis:
1. Evaluate the current China/Taiwan logistics costs.
Assume a current total volume of 190,000 CBM
and that 89 percent is shipped direct from the supplier plants in containers. Use the data from the
case and assume that the supplier-loaded containers are 85 percent full. Assume that consolidation
centers are run at each of the four port locations.
The consolidation centers use only 40-foot containers and fill them to 96 percent capacity.
Assume that it costs $480 to ship a 20-foot container and $600 to ship a 40-foot container. What
is the total cost to get the containers to the United
States? Do not include U.S. port costs in this part
of the analysis.
2. Evaluate an alternative that involves consolidating all 20-foot container volumes and using only
a single consolidation center in Shanghai/Ningbo.
Assume that all the existing 20-foot container
­volumes and the existing consolidation center volumes are sent to this single consolidation center by
suppliers. This new consolidation center volume
would be packed into 40-foot containers, filled to
96 percent, and shipped to the United States. The
existing 40-foot volume would still be shipped
direct from the suppliers at 85 percent capacity
utilization.
3. What should be done based on your analytics analysis? What have you not considered that may make
your analysis invalid or that may strategically limit
success? What do you think Grainger management
should do?
Many thanks to Gary Scalzitti of Grainger for help with developing this case.
424
Section 3
Supply Chain Processes
Practice Exam
In each of the following, name the term defined. Answers
are listed at the bottom.
1. Refers to how common an item is or how many substitutes might be available.
2. When a customer allows the supplier to manage
inventory policy for an item or group of items.
3. A phenomenon characterized by increased variation
in ordering as we move from the customer to the
manufacturer in the supply chain.
4. Products that satisfy basic needs and do not change
much over time.
5. Products with short life cycles and typically high
profit margins.
6. A supply chain that must deal with high levels of
both supply and demand uncertainty.
7. In order to cope with high levels of supply uncertainty, a firm would use this strategy to reduce risk.
8. Used to describe functions related to the flow of
material in a supply chain.
9. When a firm works with suppliers to look for opportunities to save money and benefit the environment.
10. Refers to an estimate of the cost of an item that
includes all costs related to the procurement and use
of an item, including the costs of disposing after its
useful life.
Answers To Practice Exam 1. Specificity 2. Vendor-managed inventory 3. Bullwhip effect 4. Functional products 5. Innovative products
6. Agile supply chain 7. Multiple sources of supply (pooling) 8. Logistics 9. Green sourcing 10. Total cost of ownership
Supply and Demand
Planning and
Control
SECTION
FOUR
17. Enterprise Resource Planning Systems
18. Forecasting
19. Sales and Operations Planning
20. Inventory Management
21. Material Requirements Planning
22. Workcenter Scheduling
23. Theory of Constraints
I n f o rmatio n Te c hnology Plays an
I mpo rtant Ro le in O p e rations an d
S u pply C hain Manage me nt Suc ce ss
Running a business requires a great planning system. What do we expect to sell in the future? How
many people should we hire to handle the Christmas
rush? How much inventory do we need? What
should we make today? This section discusses various approaches used to answer these questions.
The use of comprehensive software packages is
common practice, but it is important to understand
the basic planning concepts that underlie them so
that the right software can be purchased and configured correctly. Moreover, given this basic understanding, a spreadsheet can be created for simple
production planning situations.
425
17
Enterprise
Resource
Planning Systems
Learning Objectives
LO17–1
LO17–2
LO17–3
LO17–4
Understand what an enterprise resource planning (ERP) system is.
Explain how ERP integrates business units through information sharing.
Illustrate how supply chain planning and control fits within ERP.
Evaluate supply chain performance using data from the ERP system.
ERP IN T HE CLOUD!
Imagine having your PC, your cell phone, and your iPad all being in sync—all the
time. Imagine being able to access all of your personal data, your bank accounts,
your investments, or the location of your partner at any given moment. Imagine having the ability to organize and retrieve data from any online source. Imagine being
able to share that data—photos, movies, contracts, e-mail, documents, and so forth—
with your friends, family, and co-workers in an instant. Imagine being able to do this
Cloud computing
A term that refers to
delivering hosted ERP
services over the Internet.
This can significantly
reduce the cost of ERP.
without being tethered to an Ethernet cable. Everything is wireless and security is
ensured. This is what personal cloud computing promises to deliver.
Now move this into the business realm. Companies can make all of their data available through simple apps. Every employee, no matter where they are located, can
set up an instant office with a simple and secure wireless
connection. New applications are instantly deployed globally to all employees when they are ready. All employees
are looking at the same data, using the same application
software, and reacting to the same real-time information.
The savings on cabling, on server utilization, training, and
support are dramatic. But the real benefits come from optimization and more consistent decisions, sharing customer
information, and transparency from knowing the exact current status of the firm. Welcome to the world of ERP and
working in “the cloud.”
© Ronda Churchill/Bloomberg via Getty Images
426
Enterprise Resource Planning Systems
Chapter 17
This chapter discusses the integrated enterprise resource planning (ERP) systems that
are now commonly used by large companies to support supply and demand planning and
control, the topic of this section of the book. Major software vendors such as JDA Software,
Microsoft, Oracle, and SAP (see Exhibit 17.1) offer state-of-the-art systems designed to provide real-time data to support better routine decision making, improve the efficiency of transaction processing, foster cross-functional integration, and provide improved insights into how
a business should be run.
In most companies, ERP provides the information backbone needed to manage day-today execution. These systems support the standard planning and control functions covered
in this section of the book. In particular, standard applications include forecasting covered
in Chapter 18, sales and operations planning in Chapter 19, inventory control in Chapter
20, material requirements planning in Chapter 21, and workcenter scheduling in Chapter 22.
The standard offering from the major vendors are often extended through more specialized
industry-specific applications, or through custom modules built with spreadsheets or other
general-purpose software.
427
Enterprise resource
planning (ERP)
A computer system that
integrates application
programs in accounting,
sales, manufacturing, and
the other functions in a
firm. This integration is
accomplished through a
database shared by all the
application programs.
WHAT IS ERP?
The term enterprise resource planning (ERP) can mean different things, depending on one’s
viewpoint. From the view of managers in a company, the emphasis is on the word planning; ERP represents a comprehensive software approach to support decisions concurrent
with planning and controlling the business. On the other hand, for the information technology
community, ERP is a term describing a software system that integrates application programs
in finance, manufacturing, logistics, sales and marketing, human resources, and other functions in a firm. This integration is accomplished through a database shared by all the functions and data-processing applications. ERP systems typically are very efficient at handling
the many transactions that document the activities of a company. For our purposes, we begin
by describing our view of what ERP should accomplish for management, with an emphasis
on planning. Following this, we describe how the ERP software programs are designed and
then provide points to consider in choosing an ERP system. Our special interest is in how the
software supports supply chain planning and control decisions.
ERP systems allow for integrated planning across the functional areas in a firm. Perhaps
more importantly, ERP also supports integrated execution across functional areas. Today, the
focus is moving to coordinated planning and execution across companies. In many cases, this
work is supported by ERP systems.
C o n s is t e nt N um be r s
ERP requires a company to have consistent definitions across functional areas. Consider the
problem of measuring demand. How is demand measured? Is it when manufacturing completes an order? When items are picked from finished goods? When they physically leave the
ex hibit 17.1
Major ERP Vendors
Company
Special Features
Website
JDA Software
Recent growth through purchase of software companies including i2 and Manugistics. Specializes in supply chain applications.
www.jda.com
Microsoft
Windows integration and the Office suite (Word, Excel,
PowerPoint). The ERP product is Microsoft Dynamics that
features customer relationship management.
www.microsoft.com
Oracle
Major database vendor (hardware and software).
www.oracle.com
SAP
Largest ERP vendor. Comprehensive scope of products across
many industries.
www.sap.com
LO 17-1
Understand what an
enterprise resource
planning (ERP) system is.
428
Supply and Demand Planning and Control
Section 4
premises? When they are invoiced? When they arrive at the customer sites? What is needed
is a set of agreed-on definitions that are used by all functional units when they are processing
their transactions. Consistent reporting of such measures as demand, stockouts, raw materials inventory, and finished goods inventory, for example, can then be accomplished. This is a
basic building block for ERP systems.
Companies implementing ERP strive to derive benefits through much greater efficiency
gained by an integrated supply chain planning and control process. In addition, better responsiveness to the needs of customers is obtained through the real-time information provided by
the system. To better understand how this works, we next describe features of ERP software.
S oftwa r e Imp erat ives
There are four aspects of ERP software that determine the quality of an ERP system:
1.
2.
3.
4.
The software should be multifunctional in scope with the ability to track financial
results in monetary terms, procurement activity in units of material, sales in terms
of product units and services, and manufacturing or conversion processes in units of
resources or people. That is, excellent ERP software produces results closely related
to the needs of people for their day-to-day work.
The software should be integrated. When a transaction or piece of data representing
an activity of the business is entered by one of the functions, data regarding the other
related functions are updated as well. This eliminates the need for reposting data to
the system. Integration also ensures a common vision—we all sing from the same
sheet of music.
The software needs to be modular in structure so it can be combined into a single
expansive system, narrowly focused on a single function, or connected with software
from another source/application.
The software must facilitate basic planning and control activities, including forecasting, production planning, and inventory management.
An ERP system is most appropriate for a company seeking the benefits of data and process
integration supported by its information system. Benefit is gained from the elimination of
redundant processes, increased accuracy in information, superior processes, and improved
speed in responding to customer requirements.
An ERP software system can be built with software modules from different vendors, or it
can be purchased from a single vendor. A multivendor approach can provide the opportunity
to purchase “best in class” of each module. But this is usually at the expense of increased cost
and greater resources that may be needed to implement and integrate the functional modules.
On the other hand, a single-vendor approach may be easier to implement, but the features and
functionality may not be the best available.
Routine De cisio n Makin g
Transaction processing
This is the posting and
tracking of the detailed
activities of a business.
Decision support
This is the ability of the
system to help a user make
intelligent judgments about
how to run the business.
It is important to make a distinction between the transaction processing capability and the
decision support capability of an ERP system. Transaction processing relates to the posting
and tracking of the activities that document the business. When an item is purchased from
a vendor, for example, a specific sequence of activities occurs. The solicitation of the offer,
acceptance of the offer, delivery of goods, storage in inventory, and payment for the purchase
are all activities that occur as a result of the purchase. The efficient handling of the transactions as goods move through each step of the process is the primary goal of an ERP system.
A second objective of an ERP system is decision support. Decision support relates to how
well the system helps the user make intelligent judgments about how to run the business. A
key point here is that people, not software, make the decisions. The system supports better
decision making. In the case of purchasing an item, for example, the amount to purchase,
the selection of the vendor, and how it should be delivered will need to be decided. These
decisions are made by professionals, while ERP systems are oriented toward transaction processing. However, over time, they evolve using decision logic based on parameters set in the
Enterprise Resource Planning Systems
Chapter 17
429
system. For example, for items stored in inventory, the specific reorder points, order quantities, vendors, transportation vendors, and storage locations can be established when the items
are initially entered in the system. At a later point, the decision logic can be revisited to
improve the results. A major industry has been built around the development of bolt-on software packages designed to provide more intelligent decision support to ERP systems.
HOW ERP CONNECTS THE FUNCTIONAL UNITS
A typical ERP system is made up of functionally oriented and tightly integrated modules. All
LO 17-2
the modules of the system use a common database that is updated in real time. Each module
Explain how ERP integrates
has the same user interface, similar to that of the familiar Microsoft Office products, thus
business units through
making the use of the different modules much easier for users trained on the system. ERP sysinformation sharing.
tems from various vendors are organized in different ways, but typically modules are focused
on at least the following four major areas: finance, manufacturing and logistics, sales and
marketing, and human resources.
ERP systems have evolved in much the same way as car models at automobile manufacturers. Automakers introduce new models every year or two
and make many minor refinements. Major (platform) changes are made much
less frequently, perhaps every five to eight years. The same is true of ERP
software. ERP vendors are constantly looking for ways to improve the functionality of their software, so new features are often added. Many of these
minor changes are designed to improve the usability of the software through
a better screen interface or added features that correspond to the “hot” idea
of the time. Major software revisions that involve changes to the structure of
the database, and changes to the network and computer hardware technologies, though, are made only every three to five years. The basic ERP platform
cannot be easily changed because of the large number of existing users and
support providers. But these changes do occur.
Exhibit 17.2 depicts the scope of ERP applications. The diagram is meant
to show how a comprehensive information system uses ERP as its core or © Jag_cz/Shutterstock.com
ex hibit 17.2
The Scope of ERP Applications
Enterprise
Resource Planning
Manufacturing and logistics
Manufacturing
planning and control
Sales and operations
planning
Material and capacity
planning
Material and vendor
management
Enterprise planning
models
Enterprise
performance
Data
warehousing
Report generation
Transaction
processing
Human resource
management
Finance
Sales and marketing
430
Supply and Demand Planning and Control
Section 4
backbone. Many other software-based functions may be integrated with the ERP system but
are not necessarily included in the ERP system. The use of more specialized software such
as decision support systems can often bring significant competitive advantages to a firm. The
following brief descriptions of typical module functionality give an indication of how comprehensive the applications can be.
Fina nce
As a company grows through acquisition, and as business units make more of their own decisions, many companies find themselves with incompatible and sometimes conflicting financial data. An ERP system provides a common platform for financial data capture, a common
set of numbers, and processes, facilitating rapid reconciliation of the general ledger. The real
value of an ERP system is in the automatic capture of basic accounting transactions from the
source of the transactions. The actual order from a customer, for example, is used not only
by manufacturing to trigger production requirements, but also becomes the information for
updating accounts payable when the order is actually shipped.
M a nufa ctu rin g an d Lo gistics
This set of applications is the largest and most complex of the module categories. The system
components discussed in this section of the book are concentrated in this area. Typical components include:
∙
∙
∙
∙
∙
∙
Sales and operations planning coordinates the various planning efforts, including
marketing planning, financial planning, operations planning, and human resource
planning.
Materials management covers tasks within the supply chain, including purchasing,
vendor evaluation, and invoice management. It also includes inventory and warehouse
management functions to support the efficient control of materials.
Plant maintenance supports the activities associated with planning and performing
repairs and preventative maintenance.
Quality management software implements procedures for quality control and
assurance.
Production planning and control supports both discrete and process manufacturing.
Repetitive and configure-to-order approaches are typically provided. Most ERP systems address all phases of manufacturing, including capacity leveling, material requirements planning, just-in-time (JIT), product costing, bill of materials processing, and
database maintenance. Orders can be generated from sales orders or from links to an
Internet site.
Project management systems facilitate the setup, management, and evaluation of
large, complex projects.
S a le s a n d Ma rket in g
This group of system components supports activities such as customer management; sales
order management; forecasting, order management, credit checking configuration management; distribution, export controls, shipping, transportation management; and billing,
invoices, and rebate processing. These modules, like the others, are increasingly implemented
globally, allowing firms to manage the sales process worldwide. For example, if an order is
received in Hong Kong, but the products are not available locally, they may be internally procured from warehouses in other parts of the world and shipped to arrive together at the Hong
Kong customer’s site.
H um a n Re so u rces
This set of applications supports the capabilities needed to manage, schedule, pay, hire, and
train the people who make an organization run. Typical functions include payroll, benefits
Enterprise Resource Planning Systems
Chapter 17
431
administration, hiring procedures, personnel development planning, workforce planning,
schedule and shift planning, time management, and travel expense accounting.
C u st om iz e d S oftwa r e
In addition to the standard application modules, many companies utilize special add-on modules that link to the standard modules, thus tailoring applications to specific needs. These
modules may be tailored to specific industries such as chemical/petrochemical, oil and gas,
hospital, or banking. They may also provide special decision support functions such as optimal scheduling of critical resources.
Even though the scope of applications included in standard ERP packages is very large,
additional software will usually be required because of the unique characteristics of each
company. A company generates its own unique mix of products and services that are designed
to provide a significant competitive advantage to the firm. This unique mix of products and
services will need to be supported by unique software capabilities, some of which may be
purchased from vendors and some that will need to be custom-designed. Customized software
applications are also widely used to coordinate the activities of a firm with its supply chain
customers and suppliers.
D at a I n t e gr a tion
The software modules, as described earlier, form the core of an ERP system. This core is
designed to process the business transactions to support the essential activities of an enterprise in an efficient manner. Working from a single database, transactions document each of
the activities that compose the processes used by the enterprise to conduct business. A major
value of the integrated database is that information is not reentered at each step of a process,
thus reducing errors and work.
Transactions are processed in real time, meaning that as soon as the transaction is entered
into the system, the effect on items such as inventory status, order status, and accounts receivable is known to all users of the system. There is no delay in the processing of a transaction in
a real-time system. A customer could, for example, call into an order desk to learn the exact
status of an order—or determine the status independently through an Internet connection. From
a decision analysis viewpoint, the amount of detail available in the system is extremely rich. If,
for example, one wishes to analyze the typical lead time for a make-to-order product, the analyst
could process an information request that selects all of the orders for the product over the past
three months, calculate the time between order date and delivery date for each order, and finally
average the time for the whole set of orders. Analyses, such as this lead time, can be valuable for
evaluating improvements designed to make the process more responsive, for example.
To facilitate queries not built into the standard ERP system software, a separate data
warehouse is commonly employed. A data warehouse is a special program (often running on a
totally separate computer) that is designed to automatically archive and process data for uses that
are outside the basic ERP system applications. For example, the data warehouse could, on an ongoing basis, perform the calculations needed for the average lead time question. The data warehouse
software and database is set up so that users may access and analyze data without placing a burden
on the operational ERP system. This is a powerful mechanism to support higher-level decision
support applications. See the nearby OSCM at Work box titled “Open Information Warehouse.”
A good example of a company making use of a data warehouse is Walmart. Walmart is
now able to put two full years of retail store sales data online. The data are used by both
internal Walmart buyers and outside suppliers—sales and current inventory data on products sold at Walmart and Sam’s Club stores. Vendors, who are restricted to viewing products
they supply, use a Web-based extranet site to collaborate with Walmart’s buyers in managing
inventory and making replenishment decisions. A vendor’s store-by-store sales results for a
given day are available to vendors by 4 A.M. the following day. The database is more than 130
terabytes in size. Each terabyte is the equivalent of 250 million pages of text. At an average of
500 pages per book, a terabyte is a half-million books. For Walmart as a whole, that is about
20 major university libraries.
Real time
As soon as a transaction
is entered, the effect is
known by all users of the
system.
Data warehouse
A special program that is
designed to automatically
capture and process data
for uses that are outside
the basic ERP system
applications.
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Supply and Demand Planning and Control
Section 4
OSCM AT WORK
Open Information Warehouse
Sales
Q1
Q2
Q3
Q4
Total
S. Paolo
500
600
300
500
1,900
S. Vialli
700
600
200
700
2,200
S. Ferrari
600
700
400
700
2,400
S. Corleone
200
700
700
900
2,500
2,000
2,600
1,600
2,800
9,000
Any modern database will let you easily formulate an SQL
query like “What sales did my company have in Italy in 2016?”
A report generated in response to such a query could look
like this:
Region
Q1
Q2
Q3
Q4
Total
Total
Umbria
1,000
1,200
800
2,000
5,000
Toscana
2,000
2,600
1,600
2,800
9,000
Calabria
400
300
150
450
1,300
3,400
4,100
2,550
5,250
15,300
Total
But things get more complex if, for instance, we then
want to use this answer as the basis for drilling down to look
at the sales for different quarters and sales representatives in
the various regions. Drilling down means descending through
an existing hierarchy to bring out more and more detail.
In the following example, we drill down through the
sales hierarchy (sales representatives in Toscana). Signore
Corleone’s sales do not appear to have been affected by
the holiday season in the third quarter.
At this point, you can switch to another dimension—for
instance, from sales representative to product sold. This is
often referred to as slice and dice.
Product
Q1
Q2
Q3
Q4
Total
X-11
2,000
2,500
1,500
3,550
9,550
Z-12
1,400
1,600
1,050
1,700
5,750
Total
3,400
4,100
2,550
5,250
15,300
From the standpoint of a data analyst, it can now be
useful to check sales of particular products in each region.
Current software allows the end user to do this easily using
the data warehouse approach implemented within the
system.
HOW SUPPLY CHAIN PL ANNING AND CONTROL FITS
WITHI N ERP
LO 17-3
Illustrate how supply chain
planning and control fits
within ERP.
ERP is concerned with all aspects of a supply chain, including managing materials, scheduling machines and people, and coordinating suppliers and key customers. The coordination
required for success runs across all functional units in the firm. Consider the following simple
example to illustrate the degree of coordination required.
S im plifie d E xamp le
© DJC/Alamy
Ajax Food Services Company has one plant that makes sandwiches. These are sold in vending
machines, cafeterias, and small stores. One of the sandwiches is peanut butter and jelly (PBJ).
It is made from bread, butter, peanut butter, and grape jelly. When complete, it
is wrapped in a standard plastic package used for all Ajax sandwiches. One loaf
of bread makes 10 sandwiches, a package of butter makes 50 sandwiches, and
containers of peanut butter and jelly each make 20 sandwiches.
Consider the information needed by Ajax for planning and control. First,
Ajax needs to know what demand to expect for its PBJ sandwich in the future.
This might be forecast by analyzing detailed sales data from each location
where the sandwiches are sold. Because sales are all handled by sales representatives who travel between the various sites, data based on the actual orders
and sales reports provided by the reps can be used to make this forecast. The
same data are used by human resources to calculate commissions owed to the
reps for payroll purposes. Marketing uses the same data to analyze each current
location and evaluate the attractiveness of new locations.
Freshness is very important to Ajax, so daily demand forecasts are developed to plan sandwich making. Consider, for example, that Ajax sees that it
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Chapter 17
needs to make 300 PBJ sandwiches to be delivered to the sales sites this Friday. Ajax will
actually assemble the sandwiches on Thursday. According to the usage data given earlier, this
requires 30 loaves of bread, 6 packages of butter, and 15 containers of peanut butter and jelly.
Freshness is largely dictated by the age of the bread, so it is important that Ajax works closely
with the local baker because the baker delivers bread each morning on the basis of the day’s
assembly schedule. Similarly, the delivery schedules for the butter, peanut butter, and jelly
need to be coordinated with the vendors of these items.
Ajax uses college students who work on a part-time basis to assemble the sandwiches.
A student can make 60 sandwiches per hour and sandwiches must be ready for loading into
the delivery trucks by 4:00 P.M. on the day prior to delivery. Our 300 sandwiches require five
hours of work, so any one student doing this work needs to start at or before 11:00 A.M. on
Thursday to make the sandwiches on time.
An ERP system is designed to provide the information and decision support needed to
coordinate this type of activity. Of course, with our simplified example, the coordination is
trivial, but consider if our company were making hundreds of different types of sandwiches
in 1,000 cities around the world, and these sandwiches were sold at hundreds of sites in each
of these cities. This is exactly the scale of operations that can be handled by a modern ERP
system.
Precisely how all of these calculations are made is, of course, the main focus of this section of the book. All of the details for how material requirements are calculated, capacity is
planned, and demand forecasts are made, for example, are explained in great detail.
SA P S u p ply Cha in M a na g e men t
In this section, we see how SAP, a major ERP vendor, has approached the details of supply
chain planning and control. Here, we are using SAP to show how one vendor organizes the
functions. Other major vendors like JDA Software, Oracle, and Microsoft each have a unique
approach to packaging supply chain software.
SAP divides its supply chain software into four main functions: supply chain planning,
supply chain execution, supply chain collaboration, and supply chain coordination. Current
information about products is on vendors’ Websites, and readers are encouraged to download
the white papers that describe a vendor’s current thinking. These publications are informative
and indicate where a vendor will move in the future. Moreover, comparing/contrasting this
information can be very educational—and help in making key choices as to which business
processes can be supported by standard (plain vanilla) software.
The supply chain design module provides a centralized overview of the entire supply chain and key performance indicators, which helps identify weak links and potential
improvements. It supports strategic planning by enabling the testing of various scenarios
to determine how changes in the market or customer demand can be addressed by the supply chain. Here, for our simplified example of Ajax food services, we could evaluate the
relative profitability of particular market channels and locations such as vending machines
versus shops in train stations.
Collaborative demand and supply planning helps match demand to supply. Demandplanning tools take into account historical demand data, causal factors, marketing events,
market intelligence, and sales objectives and enable the supply chain network to work on
a single forecast. Supply planning tools create an overall supply plan that covers materials
management, production, distribution and transportation requirements, and constraints. Here,
Ajax would be able to anticipate the demands for each kind of sandwich in each location and
plan replenishments accordingly.
SA P S u p ply Cha in Exe cu tio n
Materials management shares inventory and procurement order information to ensure that the
materials required for manufacturing are available in the right place and at the right time. This
set of applications supports plan-driven procurement, inventory management, and invoicing,
with a feedback loop between demand and supply to increase responsiveness. In this set of
applications, Ajax would plan for all the sandwich components to be delivered to the right
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Supply and Demand Planning and Control
places at the right times. Inventories might be maintained on some items such as peanut butter, while others such as bread might be planned on a just-in-time basis.
Collaborative manufacturing shares information with partners to coordinate production
and enable everyone to work together to increase both visibility and responsiveness. These
applications support all types of production processes: engineer-to-order, assemble-to-order,
make-to-order, and make-to-stock. They create a continuous information flow across engineering, planning, and execution and can optimize production schedules across the supply
chain, taking into account material and capacity constraints. Here, Ajax might do joint planning with key suppliers and perhaps organize the planning of special promotions.
Collaborative fulfillment supports partnerships that can intelligently commit to delivery
dates in real time and fulfill orders from all channels on time. This set of applications includes
a global available-to-promise (ATP) feature that locates finished products, components, and
machine capacities in a matter of seconds. It also manages the flow of products through sales
channels, matching supply to market demand, reassigning supply and demand to meet shifts
in customer demand, and managing transportation and warehousing. Clearly, all these logistics activities are critical to Ajax in order to deliver fresh sandwiches in the right amounts.
SAP S up p ly C h ain C o llabo ratio n
The inventory collaboration hub uses the Internet to gain visibility to suppliers and manage
the replenishment process. Suppliers can see the status of their parts at all plants, receive
automatic alerts when inventory levels get low, and respond quickly via the Web. The hub can
also be integrated with back-end transaction and planning systems to update them in real time.
Here, Ajax could provide real-time inventory views to its suppliers—not only of material suppliers, but also of downstream inventories (i.e., sandwiches).
Collaborative replenishment planning is particularly useful in the consumer products
and retail industries. These applications allow manufacturers to collaborate with their strategic retail customers to increase revenue, improve service, and lower inventory levels and
costs. They enable an exception-based collaborative planning, forecasting, and replenishment
(CPFR) process that allows the firm to add retail partners without a proportional increase in
staff. This set of applications would be particularly useful to Ajax as it grows its global business and adds new channels of distribution.
Vendor managed inventory (VMI) is a set of processes to enable vendor-driven replenishment that can be implemented over the Web. Now, Ajax vendors would no longer receive
“orders.” They would replenish Ajax inventories as they like—but be paid for their materials
only when items are consumed by Ajax.
Enterprise portal gives users personalized access to a range of information, applications,
and services supported by the system. It uses role-based technology to deliver information to
users according to their individual responsibilities within the supply chain network. It can also
use Web-based tools to integrate third-party systems in the firm’s supply chain network. Here,
for example, marketing people at Ajax might like to examine the detailed sales data (and perhaps customer questionnaires) in relation to a new product introduction.
Mobile supply chain management is a set of applications so that people can plan, execute,
and monitor activity using mobile and remote devices. Mobile data entry using personal data
assistant devices and automated data capture using wireless “smart tags,” for example, are
supported. Here, Ajax can have marketing and even delivery personnel report on actual store
conditions—not just sales but also category management. For example, how well does the
actual assortment of sandwiches match the standard?
SAP S up p ly C h ain C o o rdin atio n
Supply chain event management monitors the execution of supply chain events, such as the
issue of a pallet or the departure of a truck, and flags any problems that come up. This set
of applications is particularly useful for product tracking/traceability. For Ajax, if there is a
customer complaint about a sandwich, it is critical to quickly determine if this is an isolated
instance or whether there might be a large group of bad quality sandwiches—and how to
find them.
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435
Supply chain performance management allows the firm to define, select, and monitor key
performance indicators, such as costs and assets, and use them to gain an integrated, comprehensive view of performance across the supply chain. It provides constant surveillance of key
performance measures and generates an alert if there is a deviation from plan. It can be used
with mySAP Business Intelligence and SAP’s data warehousing and data analysis software.
Here, Ajax needs to not only assess profit contribution by sandwich type and location, it also
needs to determine which are the best supplier and customer partners.
PER FORMANCE MET RICS TO EVALUATE INTEGRATED
SYSTEM EFFECTIVENESS
As indicated, one significant advantage that a firm gains from using an integrated ERP system
is the ability to obtain current data on how the firm is performing. An ERP system can provide the data needed for a comprehensive set of performance measures to evaluate strategic
alignment of the various functions with the firm’s strategy. An example of the comprehensiveness of the measures is tracking the time from spending cash on purchases until the cash
is received in sales.
The balance sheet and the income and expense statements contain financial measures, such
as net profit, that traditionally have been used to evaluate the success of the firm. A limitation
of traditional financial metrics is that they primarily tell the story of past events. They are less
helpful as a guide to decision makers in creating future value through investments in customer
infrastructure, suppliers, employees, manufacturing processes, and other innovations.
Our goal is a more holistic approach to management of the firm. Exhibit 17.3 depicts three
major functional areas that make up the internal supply chain of a manufacturing enterprise:
purchasing, manufacturing, and sales and distribution. Tight cooperation is required between
these three functions for effective manufacturing planning and control. Considered independently, purchasing is mainly concerned with minimizing materials cost, manufacturing with
minimum production costs, sales with selling the greatest amount, and distribution with minimum distribution and warehousing costs. Let us consider how each independently operating
function might seek to optimize its operation.
T h e “ Fu nctiona l S ilo” A p p ro ach
The purchasing function is responsible for buying all of the material required to support
manufacturing operations. When operating independently, this function wishes to know what
materials and quantities are going to be needed over the long term. The purchasing group then
solicits bids for the best price for each material. The main criterion is simply the cost of the
material, and the purchasing function is evaluated on this criterion: What is latest actual cost
versus standard cost? Of course, quality is always going to be important to the group, so typically some type of quality specification will need to be guaranteed by the supplier. But quality
is more of a constraint than a goal; suppliers must achieve some minimal level of specification. Consideration of delivery schedules, quantities, and responsiveness are also important,
ex hibit 17.3
Manufacturing Operating Cycle
Procurement
cycle
Manufacturing
cycle
Sales and distribution
cycle
· Purchase cost of material
· Accounts payable
· Raw materials inventory
· Work-in-process
· Finished goods inventory
· Distribution inventory
· Accounts receivable
LO 17-4
Evaluate supply chain
performance using data
from the ERP system.
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Supply and Demand Planning and Control
but again these considerations are often secondary at best in how the purchasing function is
evaluated in a traditional firm.
For manufacturing, making the product at the lowest possible cost is the classic metric. To
do this requires minimum equipment downtime, with high equipment and labor utilization.
Stopping to set up equipment is not the desire of this group. This group is focused on highvolume output, with minimum changeovers. Quality is again “important”—but as in purchasing, it is more of a minimum hurdle.
Long production runs lead to lower unit costs, but they also generate larger inventories. For
sales, larger inventories appear at first to be desirable, since these should support customer
service. Alas, it is not so; a one-year supply of product A is of no help when we are out of
product B.
Distribution can be equally narrow-minded and suboptimal. In the classic case, its job is
moving the product from the manufacturing site to the customer at the lowest possible cost.
Depending on the product, it may need to be stored in one or more distribution centers and
be moved via one or more different modes of transportation (truck, rail, etc.). Evaluation of
activities tends to focus on the specific activity involved. For example, many firms focus on
the lowest price quotation for moving a product from one stage of the distribution chain to
another, rather than on the total costs of moving materials into and out of the overall firm.
And even here this cost focus needs to be integrated with other objectives such as lower inventories, faster response times, and customer service.
Consider the implications if all three areas are allowed to work independently. To take
advantage of discounts, purchasing will buy the largest quantities possible. This results in
large amounts of raw material inventory. The manufacturing group desires to maximize production volumes in order to spread the significant fixed costs of production over as many
units as possible. These large lot sizes result in high amounts of work-in-process inventory,
with large quantities of goods pushed into finished goods whether they are needed or not.
Large lot sizes also mean that the time between batches increases; therefore, response times
to unexpected demand increase. Finally, distribution will try to fully load every truck that
is used to move material to minimize transportation cost. Of course, this may result in large
amounts of inventory in distribution centers (perhaps the wrong ones) and might not match
well with what customers really need. Given the opportunity, the sales group might even
sell product that cannot possibly be delivered on time. After all, they are evaluated on sales,
not deliveries. A more coordinated approach is facilitated by the use of an ERP system.
The following is an example of a consistent set of metrics useful for managing supply chain
functions effectively.
Inte gr a t e d Su p p ly Ch ain Met rics
Cash-to-cash cycle
time
The average number
of days that it takes a
business to convert cash
spent for raw material and
other resources into cash
inflows from sales.
The APICS Supply Chain Council has developed many metrics to measure the performance
of the overall supply chain. It has used these standardized measures to develop benchmarks
for comparisons between companies. Exhibit 17.4 contains a list of some of these measures
with average and best-in-class benchmarks. The average and best-in-class measures are for
typical large industrial products. The APICS Supply Chain Council has developed sets of
measures similar to these for many different categories of companies.
A particularly useful approach to measuring performance not only captures the integrated
impact that the three classic functions have on the entire business supply chain, it also integrates the finance function. Such a metric, which measures the relative efficiency of a supply
chain, is cash-to-cash cycle time. Cash-to-cash cycle time integrates the purchasing, manufacturing, and sales/distribution cycles depicted in Exhibit 17.3. But it also relates well to the
financial maxim: Cash is king! Calculating the measure requires the use of data related to
purchasing, accounting, manufacturing, and sales.
Actually, cash-to-cash cycle time is a measure of cash flow. Cash flow indicates where
cash comes from (its source), where cash is spent (its use), and the net change in cash for the
year. Understanding how cash flows through a business is critical to managing the business
effectively. Accountants use the term operating cycle to describe the length of time it takes a
business to convert cash outflows for raw materials, labor, and so forth into cash inflows. This
Enterprise Resource Planning Systems
exhibit 17.4
Chapter 17
Supply Chain Metrics
Best in Class
Average or
Median
Measure
Description
Delivery performance
What percentage of orders is shipped
according to schedule?
93%
69%
Fill rate by line item
Orders often contain multiple line
items. This is the percentage of the
actual line items filled.
97%
88%
Perfect order fulfillment
This measures how many complete
orders were filled and shipped on
time.
92.4%
65.7%
Order fulfillment lead time
The time from when an order is
placed to when it is received by the
customer.
135 days
225 days
Warranty cost of % of
revenue
This is the actual warranty expense
divided by revenue.
1.2%
2.4%
Inventory days of supply
How long an item spends in inventory
before being used.
55 days
84 days
Cash-to-cash cycle time
Considering accounts payable,
accounts receivable, and inventory,
this is the amount of time it takes to
turn cash used to purchase materials into cash from a customer.
35.6 days
99.4 days
Asset turns
This is a measure of how many times
the same assets can be used to
generate revenue and profit.
4.7 turns
1.7 turns
cycle time determines, to a large extent, the amount of capital needed to start and operate a
business. Conceptually, cash-to-cash cycle time is calculated as follows:
Cash-to-cash cycle time = Inventory days of supply + Days of sales outstanding
– Average payment period for material​​[​17.1​]​
The overall result is the number of days between paying for raw materials and getting paid
for the product. Going through the details of calculating cash-to-cash cycle time demonstrates
the power of integrated information. These calculations are straightforward in an ERP system.
The calculation can be divided into three parts: the accounts receivable cycle, the inventory
cycle, and the accounts payable cycle.
Exhibit 17.5 shows the data that are used for calculating cash-to-cash cycle time. The
data are controlled by different functions within the company. The current accounts payable
amount, an account that is dependent on the credit terms that purchasing negotiates with suppliers, captures the current money the firm owes its suppliers. As will be seen in the calculation, this is a form of credit to the company.
The inventory account gives the value of the entire inventory within the company. This includes
raw materials, work-in-process, finished goods, and distribution inventory. The value of inventory
depends on the quantities stored and also the cost of the inventory to the firm. All three major
functional areas affect the inventory account. Purchasing has a major influence on raw materials.
Manufacturing largely determines work-in-process and finished goods. Sales/distribution influences the location of finished goods—as well as the amounts, through their forecasts and orders.
Just as inventory is affected by all three functions, the cost of sales is dependent on costs
that are incurred throughout the firm. For the purposes of the cash-to-cash cycle time calculation, this is expressed as a percentage of total sales. This percentage depends on such items as
material cost, labor cost, and all other direct costs associated with the procurement of materials, manufacturing process, and distribution of the product.
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Supply and Demand Planning and Control
exhibit 17.5
Integrated ERP Data for Cash-to-Cash Cycle Time Calculation
Accounts
payable
Purchasing
Inventory
Manufacturing
Cost of sales
Sales and distribution
Sales
Cash-to-cash
cycle time
Accounts
receivable
ERP
Database
Sales are simply the total sales revenue over a given period of time. Finally, accounts
receivable is the amount owed the firm by its customers. The accounts receivable amount will
depend on the firm’s credit policy and its ability to deliver product in a timely manner. Exhibit
17.5 shows how the three major functional areas influence the cash-to-cash cycle calculation.
Ca lcula tin g th e C ash -to -C ash C ycle T ime
As noted, the first task in determining the cash-to-cash cycle time is to calculate accounts
receivable cycle time. This measures the length of time it takes a business to convert a sale
into cash. In other words, how long does it take a business to collect the money owed for
goods already sold? One way is to calculate the number of days of sales invested in accounts
receivable:
​
​Sd​​ = __
​[​17.2​]​
​S ​​
d
where
Sd = average daily sales
S = sales over d days
​AR ​​​​[ 17.3 ]​​
​
​AR​d​ = ___
​S​​
d
where
ARd = average days of accounts receivable
AR = accounts receivable
The next part of the calculation is the inventory cycle time. This is the number of days of
inventory measured relative to the cost of sales:
​
​Cd​​ = ​Sd​​CS​​​​[ 17.4 ]​​
where
Cd = average daily cost of sales
CS = cost of sales (percent)
Enterprise Resource Planning Systems
Chapter 17
​ I ​​
​
​Id​​ = __
​[ 17.5 ]​​
​C​​
d
where
Id = average days of inventory
I = current value of inventory (total)
Next, the accounts payable cycle time measures the level of accounts payable relative to
the cost of sales:
​AP ​​​​[ 17.6 ]​​
​
​APd​​ = ___
​C​​
d
where
APd = average days of accounts payable
AP = accounts payable
Finally, the cash-to-cash cycle time is calculated from the three cycle times.
​
​Cash-to-cash cycle time = ​ARd​​+ ​Id​​− ​APd​​​
​[ 17.7 ]​​
The cash-to-cash cycle time is an interesting measure for evaluating the relative supply
chain effectiveness of a firm. Some firms are actually able to run a negative value for the
measure. This implies the ability to invest in the business as needed—with no requirement for
additional funds! Metrics, such as cash-to-cash cycle time, can be efficiently reported using
ERP data. These metrics can even be reported in real time if needed.
EXAMPLE 17.1: Cash-to-Cash Cycle Time Calculation
Accounting has supplied the following information from our ERP system:
Sales over last 30 days = $1,020,000
Data:
Accounts receivable at the end of the month = $200,000
Inventory value at the end of the month = $400,000
Cost of sales = 60 percent of total sales
Accounts payable at the end of the month = $160,000
Calculate our current cash-to-cash cycle time.
SOLUTION
1, 020, 000
= ________
​
​ = 34, 000
30
d
200, 000
​ R​d​ = ___
A
​AR ​ = ______
​
​ = 5.88 days
​S​d​
34, 000
​S​d​
= __
​S ​
​ ​d​ = ​S​d​CS = 34,000(0.6) = 20,400
C
​
​​ ​​
400, 000
​I​d​ = __
​ I ​ = ______
​
​ = 19.6 days
​C​d​
20, 400
​
160, 000
​ P​d​ = ___
A
​AP ​ = ______
​
​
​C​d​
20, 400
= 7.84 days
​Cash-to-cash cycle time = AR​d​+ ​I​d​− ​AP​d​ = 5.88 + 19.6 − 7.84 = 17.64 days
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Concept Connections
LO 17-1 Understand what an enterprise resource planning (ERP) system is.
Summary
∙ ERP is a comprehensive software system that integrates data from all functional areas of a business.
This integration is accomplished through a database
that is shared by all the applications.
∙ Benefits gained are better processes, information
accuracy, and responsiveness through the real-time
information provided by the system.
∙ The system is designed to efficiently handle the
transactions that document the activities of the firm,
and also enables the users to make better business
decisions.
Key Terms
Cloud computing A term that refers to delivering hosted
ERP services over the Internet. This can significantly
reduce the cost of ERP.
Enterprise resource planning (ERP) A computer system
that integrates application programs in accounting, sales,
manufacturing, and the other functions in a firm. This
integration is accomplished through a database shared
by all the application programs.
Transaction processing This is the posting and tracking
of the detailed activities of a business.
Decision support This is the ability of the system to
help a user make intelligent judgments about how to run
the business.
LO 17-2 Explain how ERP integrates business units through information sharing.
Summary
∙ Typical ERP systems have application modules in
finance, manufacturing and logistics, sales and marketing, and human resources.
∙ The software modules connect to a common database
that is updated in real time. Data is shared across the
modules in such a way that a transaction entered in
one area is propagated to the others.
∙ In addition to the standard modules, many companies
use specialized modules that tailor the system to their
specific needs.
Key Terms
Real time As soon as a transaction is entered, the effect
is known by all users of the system.
Data warehouse A special program that is designed to
automatically capture and process data for uses that are
outside the basic ERP system applications.
LO 17-3 Illustrate how supply chain planning and control fits within ERP.
Summary
∙ Applications for supply chain activities such as managing materials, scheduling machines and people,
coordinating suppliers, and processing customer
orders are all included within an ERP system.
∙ The activities commonly supported are: design of the
supply chain system, future planning to meet supply
and demand objectives, execution of activities to meet
these activities, collaboration between suppliers and
customers, and coordination to track activities against
plans.
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441
LO 17-4 Evaluate supply chain performance using data from the ERP system.
Summary
∙ Performance measures that span functional areas are
most useful to ensure that each area is not optimizing
their own processes at the expense of the other areas.
For example, manufacturing might minimize cost by
focusing on high-volume production, with minimum
changeovers. This may result in producing too much
of one item and not enough of another, thus not allowing sales to fill customer orders.
∙ The APICS Supply Chain Council is a good source for
data relating to the metrics commonly used in different
industries. Cash-to-cash cycle time is a useful supply
chain metric because it captures how quickly a dollar
spent on raw material is converted into income from
the firm’s customers. It is calculated from accounting
data captured by the ERP system.
Key Terms
Cash-to-cash cycle time The average number of days
material and other resources into cash inflows from
sales.
that it takes a business to convert cash spent for raw
Key Formulas
​[​17.1​]​​ Cash-to-cash cycle time = Inventory days of supply +
​ ​Days of sales outstanding
​−​Average payment period for material
​AP ​​
​[​17.2​]​​​​Sd​​ = __
​S ​​​​[ 17.4 ]​​​​Cd​​ = ​Sd​​CS​​​​[ 17.6 ]​​​​AP​d​ = ___
​C​​
d
d
​AR ​​​​[ 17.5 ]​​​​Id​​ =
​[ 17.3 ]​​​​AR​d​ = ___
​Sd​​
__
​ I ​​​​[ 17.7 ]​​​​Cash-to-cash cycle time = ​AR​d​+ ​I​d​− ​AP​d​
​Cd​​
Solved Problems
LO17-4
Midwest Baking Products manufactures a variety of dry goods used in industrial and consumer baking. As the company has grown, it has found it increasingly difficult to keep accurate tabs on inventory and cash flows. Six months ago, it completed an ERP implementation
project, and the ERP system is running smoothly now. The information systems department is
training various functional areas about how to retrieve reports from the system, and the result
of one report shows the following data from the prior month (May).
Gross sales
$1,440,000
Cost of goods sold
720,000
Accounts receivable (end-of-month)
250,000
Accounts payable (end-of-month)
150,000
Net assets
3,754,000
Inventory value (end-of-month)
470,000
Use this report to calculate the cash-to-cash cycle time. Round interim calculations to
two decimal places if needed.
Solution
We calculate the cash-to-cash cycle time by using formulas 17.2 through 17.7, in order. Equation 17.7 will give us the cash-to-cash cycle time.
Average Daily Sales
1, 440, 000
​Sd​​ = __
​S ​ = ________
​
​ = 46, 451.61​
d
31
[Unlike Example 17.1, we use 31 in the denominator of the given equation because May has
31 days.]
442
Supply and Demand Planning and Control
Section 4
Average Days Accounts Receivable
250, 000
​A ​Rd​​ = ___
​AR ​ = ________
​
​ = 5.38​
​Sd​​
46, 451.61
Inventory Cycle Time
Equation 17.4 is used here, and it asks for the cost of sales as a percent of total sales. We
instead have the cost of goods sold (same as cost of sales) in dollars. We first need to convert
this to a percentage to use Equation 17.4.
720, 000
1, 440, 000
​CS = ________
​ COGS ​= ________
​
​= 0.50​
Total Sales
Now we can apply Equation 17.4:
​Cd​​ = ​Sd​​∗ CS = 46, 451.61 * 0.50 = 23, 225.81​
Average Days of Inventory
470, 000
​Id​​ = __
​ I ​ = ________
​
​ = 20.24​
​Cd​​
23, 225.81
Accounts Payable Cycle Time
150, 000
​A​Pd​​ = ___
​AP ​ = ________
​
​ = 6.46​
​Cd​​
23, 225.81
Cash-to-Cash Cycle Time
​A​Rd​​+ ​Id​​+ A​Pd​​= 5.38 + 20.24 − 6.46 = 19.16 days​
The cash-to-cash cycle time based on this recent report is 19.16 days.
Discussion Questions
LO17-2
1.
2.
3.
4.
LO17-3
5.
LO17-4
6.
7.
LO17-1
8.
Describe the benefits of using an ERP system.
Are the ERP systems discussed in the chapter appropriate for use in all firms? Explain.
Describe how an ERP system fits into the overall information system structure in a firm.
ERP systems provide a wealth of information that can be used and analyzed in a wide variety of ways. What is an inherent risk with so much information?
Visit the vendors’ Websites to read up on both SAP and Microsoft Dynamics ERP systems.
Provide a list of four ways in which the two differ in their approach to implementing ERP.
Briefly describe how supply chain planning and control is managed in an ERP system.
Explain how an ERP system can improve the evaluation and analysis of performance
metrics.
Why is the cash-to-cash cycle time such an important supply chain performance measure?
Objective Questions
LO17-1
LO17-2
1. What company is the largest ERP vendor?
2. What term relates to the posting and tracking of activities that document a business?
3. Is it true that, for an ERP system to be effective, it must be completely purchased from a
single vendor?
4. ERP systems from different vendors vary quite a bit, but typically they will focus on at
least which four major areas?
5. Which common ERP module category is typically the largest and most complex? (Answer
in Appendix D)
6. What is the term for a computer program often used to facilitate database queries that are
not part of a standard ERP system?
Enterprise Resource Planning Systems
LO17-3
LO17-4
Chapter 17
443
7. What are the four main functions within SAP’s supply chain software?
8. What term refers to the sharing of information with partners to coordinate production,
enabling everyone to work together to increase visibility and responsiveness?
9. What part of SAP gives users personalized access to a range of information, applications,
and services supported by the system?
10. What supply chain metric measures how many complete orders were filled and shipped
on time?
11. During the past month a firm shows the following metrics:
Average days of accounts receivable
6.75 days
Average daily cost of sales
$ 35,000
Current total value of inventory
$300,000
Current value of accounts payable
$200,000
ompute the cash-to-cash cycle time. Round to two decimal places in all of your calculaC
tions. (Answer in Appendix D)
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. A computer system that links all areas of a company
using an integrated set of application programs and a
common database.
2. The application programs are designed in accordance
with industry norms or _____.
3. True/False: Implementing an ERP system is a simple
exercise that involves loading software on a computer.
4. A term used for delivering ERP services on demand
over the Internet.
5. The name of Microsoft’s ERP offering.
6. Part of an ERP system that manages the activities
within a certain functional area.
7. A set of processes to enable vendor-driven replenish­ment.
8. A metric that measures the percentage of orders
shipped according to schedule.
Answers to Practice Exam 1. Enterprise resource planning (ERP) system 2. Best practices 3. False 4. Cloud computing 5. Microsoft Dynamics
6. Module 7. Vendor-managed inventory 8. Delivery performance
18
Forecasting
Learning Objectives
LO 18–1
LO 18–2
LO 18–3
LO 18–4
Understand how forecasting is essential to supply chain planning.
Evaluate demand using quantitative forecasting models.
Apply qualitative techniques to forecast demand.
Apply collaborative techniques to forecast demand.
FROM BEAN TO CUP: STARBUCKS GLOB AL
SUPPLY CHAIN CHALLENGE
Starbucks Corporation is the largest coffeehouse company in the world, with over
17,000 stores in more than 50 countries. The company serves some 50 million customers each week.
Forecasting demand for a Starbucks is an amazing challenge. The product line
goes well beyond drip-brewed coffee sold on demand in the stores. It includes
espresso-based hot drinks, other hot and cold drinks, coffee beans, salads, hot and
cold sandwiches and panini, pastries, snacks, and items
such as mugs and tumblers. Many of the company’s products are seasonal or specific to the locality of the store.
Starbucks-branded ice cream and coffee are also offered
at grocery stores around the world.
The creation of a single, global logistics system was
important for Starbucks because of its far-flung supply
chain. The company generally brings coffee beans from
Latin America, Africa, and Asia to the United States and
Europe in ocean containers. From the port of entry, the
“green” (unroasted) beans are trucked to storage sites,
either at a roasting plant or nearby. After the beans are
roasted and packaged, the finished product is trucked
to regional distribution centers, which range from
Starbucks Coffee in Bur
Juman Center Shopping
Mall, Dubai, United Arab
Emirates.
© Atlantide Phototravel/Corbis;
444
200,000 to 300,000 square feet in size. Coffee, however, is only one of the many products held at these distribution centers. They also
handle other items required by Starbucks retail outlets, everything from furniture
to cappuccino mix.
In the Analytics Exercise at the end of the chapter, we consider the challenging
demand forecasting problem that Starbucks must solve to be able to successfully run
this complex supply chain.
FOR ECASTING IN O PERATIONS AND SUPPLY CHA IN
MANAGEMENT
Forecasts are vital to every business organization and for every significant management decision. Forecasting is the basis of corporate planning and control. In the functional areas of
finance and accounting, forecasts provide the basis for budgetary planning and cost control.
Marketing relies on sales forecasting to plan new products, compensate sales personnel, and
make other key decisions. Production and operations personnel use forecasts to make periodic decisions involving supplier selection, process selection, capacity planning, and facility
layout, as well as for continual decisions about purchasing, production planning, scheduling,
and inventory.
In considering what forecasting approach to use, it is important to consider the purpose of
the forecast. Some forecasts are for very high-level demand analysis. What do we expect the
demand to be for a group of products over the next year, for example? Some forecasts are used
to help set the strategy of how, in an aggregate sense, we will meet demand. We will call these
strategic forecasts. Relative to the material in the book, strategic forecasts are most appropriate when making decisions related to overall strategy (Chapter 2), capacity (Chapter 5), manufacturing process design (Chapter 7), service process design (Chapter 9), location and
distribution design (Chapter 15), sourcing (Chapter 16), and in sales and operations planning
(Chapter 19). These all involve medium and long-term decisions that relate to how demand
will be met strategically.
Forecasts are also needed to determine how a firm operates processes on a day-to-day
basis. For example, when should the inventory for an item be replenished, or how much production should we schedule for an item next week? These are tactical forecasts where the
goal is to estimate demand in the relatively short term, a few weeks or months. These forecasts are important to ensure that in the short term we are able to meet customer lead time
expectations and other criteria related to the availability of our products and services.
In Chapter 7, the concept of decoupling points is discussed. These are points within the
supply chain where inventory is positioned to allow processes or entities in the supply chain to
operate independently. For example, if a product is stocked at a retailer, the customer pulls the
item from the shelf and the manufacturer never sees a customer order. Inventory acts as a buffer to separate the customer from the manufacturing process. Selection of decoupling points
is a strategic decision that determines customer lead times and can greatly impact inventory
investment. The closer this point is to the customer, the quicker the customer can be served.
Typically, a trade-off is involved where quicker response to customer demand comes at the
expense of greater inventory investment because finished goods inventory is more expensive
than raw material inventory.
Forecasting is needed at these decoupling points to set appropriate inventory levels for
these buffers. The actual setting of these levels is the topic of Chapter 20, “Inventory Management,” but an essential input into those decisions is a forecast of expected demand and the
expected error associated with that demand. If, for example, we are able to forecast demand
very accurately, then inventory levels can be set precisely to expected customer demand. On
the other hand, if predicting short-term demand is difficult, then extra inventory to cover this
uncertainty will be needed.
The same is true relative to service settings where inventory is not used to buffer demand.
Here, capacity availability relative to expected demand is the issue. If we can predict demand
in a service setting very accurately, then tactically all we need to do is ensure that we have the
LO 18–1
Understand how
forecasting is essential to
supply chain planning.
Strategic forecasts
Medium and long-term
forecasts that are used
for decisions related to
strategy and aggregate
demand.
Tactical forecasts
Short-term forecasts
used for making day-today decisions related to
meeting demand.
445
446
Section 4
Supply and Demand Planning and Control
Forecasting is critical in
determining how much
inventory to keep to
meet customer needs.
© John McBride & Company
Inc./The Image Bank/Getty
Images
appropriate capacity in the short term. When demand is not predictable, then excess capacity
may be needed if servicing customers quickly is important.
Bear in mind that a perfect forecast is virtually impossible. Too many factors in the
business environment cannot be predicted with certainty. Therefore, rather than search for
the perfect forecast, it is far more important to establish the practice of continual review of
forecasts and to learn to live with inaccurate forecasts. This is not to say that we should not
try to improve the forecasting model or methodology or even to try to influence demand
in a way that reduces demand uncertainty. When forecasting, a good strategy is to use two
or three methods and look at them from a common-sense view. Will expected changes in
the general economy affect the forecast? Are there changes in our customers’ behaviors
that will impact demand that are not being captured by our current approaches? In this
chapter, we look at qualitative techniques that use managerial judgment and also at quantitative techniques that rely on mathematical models. It is our view that combining these
techniques is essential to a good forecasting process that is appropriate to the decisions
being made.
QUANTI TATIVE FORECASTING MODELS
LO 18–2
Evaluate demand using
quantitative forecasting
models.
Time series analysis
A forecast in which past
demand data is used to
predict future demand.
Forecasting can be classified into four basic types: qualitative, time series analysis, causal
relationships, and simulation.
Qualitative techniques are covered later in the chapter. Time series analysis, the primary
focus of this chapter, is based on the idea that data relating to past demand can be used to
predict future demand. Past data may include several components, such as trend, seasonal, or
cyclical influences, and are described in the following section. Causal forecasting, which we
discuss using the linear regression technique, assumes that demand is related to some underlying factor or factors in the environment. Simulation models allow the forecaster to run through
a range of assumptions about the condition of the forecast. In this chapter, we focus on qualitative and time series techniques because these are most often used in supply chain planning
and control.
Forecasting
Chapter 18
447
C o m p on e nts of D e m a n d
In most cases, demand for products or services can be broken down into six components: average demand for the period, a trend, seasonal element, cyclical elements, random variation,
and autocorrelation. Exhibit 18.1 illustrates a demand over a four-year period, showing the
average, trend, and seasonal components and randomness around the smoothed demand curve.
Cyclical factors are more difficult to determine because the time span may be unknown or
the cause of the cycle may not be considered. Cyclical influence on demand may come from
such occurrences as political elections, war, economic conditions, or sociological pressures.
Random variations are caused by chance events. Statistically, when all the known causes
for demand (average, trend, seasonal, cyclical, and autocorrelative) are subtracted from total
demand, what remains is the unexplained portion of demand. If we cannot identify the cause
of this remainder, it is assumed to be purely random chance.
Autocorrelation denotes the persistence of occurrence. More specifically, the value
expected at any point is highly correlated with its own past values. In waiting line theory, the
length of a waiting line is highly autocorrelated. That is, if a line is relatively long at one time,
then shortly after that time we would expect the line still to be long.
When demand is random, it may vary widely from one week to another. Where high autocorrelation exists, the rate of change in demand is not expected to change very much from one
week to the next.
Trend lines are the usual starting point in developing a forecast. These trend lines are then
adjusted for seasonal effects, cyclical elements, and any other expected events that may influence
the final forecast. Exhibit 18.2 shows four of the most common types of trends. A linear trend is
obviously a straight continuous relationship. An S-curve is typical of a product growth and maturity cycle. The most important point in the S-curve is where the trend changes from slow growth
to fast growth or from fast to slow. An asymptotic trend starts with the highest demand growth
at the beginning but then tapers off. Such a curve could happen when a firm enters an existing
market with the objective of saturating and capturing a large share of the market. An exponential
curve is common in products with explosive growth. The exponential trend suggests that sales
will grow at an ever-increasing rate—an assumption that may not be safe to make.
A widely used forecasting method plots data and then searches for the curve pattern (such
as linear, S-curve, asymptotic, or exponential) that fits best. The attractiveness of this method
is that because the mathematics for the curve are known, solving for values for future time
periods is easy.
Sometimes our data do not seem to fit any standard curve. This may be due to several
causes essentially beating the data from several directions at the same time. For these cases, a
simplistic but often effective forecast can be obtained by simply plotting data.
ex hibit 18.1
Historical Product Demand Consisting of a Growth Trend and
Seasonal Demand
Seasonal
Trend
Number
of units
demanded
Average
1
2
Year
3
4
KEY IDEA
Remember that we are
illustrating long-term
patterns, so these
should be considered
when making long-term
forecasts. When making
short-term forecasts,
these patterns are often
not so strong.
448
Supply and Demand Planning and Control
Section 4
exhibit 18.2
2.2
2.1
2.0
1.9
1.8
1.7
1.6
Sales 1.5
(000) 1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
Common Types of Trends
Linear Trend
1 2 3 4 5 6 7 8 9 10 11 12
1.3
1.2
1.1
1.0
0.9
0.8
0.7
Sales
0.6
(000) 0.5
0.4
0.3
0.2
0.1
0
– 0.1
Asymptotic Trend
0
20
10
Time periods
Quarters
3.0
2.8
2.6
2.4
2.2
2.0
Sales 1.8
(000)
1.6
1.4
1.2
1.0
0.8
0.6
S-Curve Trend
70
Exponential Trend
60
50
40
Sales
(000) 30
20
10
1 2 3 4 5 6 7 8 9 10 11 12
0
1 2 3 4 5 6 7 8 9 10 11 12
Quarters
Sales
Trend
Tim e S erie s An alysis
Periods
Actual
Fitted line
Time series forecasting models try to predict the future based on past data. For example, sales
figures collected for the past six weeks can be used to forecast sales for the seventh week. Quarterly sales figures collected for the past several years can be used to forecast future quarters. Even
though both examples contain sales, different forecasting time series models would likely be used.
Exhibit 18.3 shows the time series models discussed in the chapter and some of their characteristics. Terms such as short, medium, and long are relative to the context in which they
are used. However, in business forecasting short term usually refers to under three months;
medium term, three months to two years; and long term, greater than two years. We would
generally use short-term forecasts for tactical decisions such as replenishing inventory or
scheduling employees in the near term, and medium-term forecasts for planning a strategy for
meeting demand over the next six months to a year and a half. In general, the short-term models compensate for random variation and adjust for short-term changes (such as consumers’
responses to a new product). They are especially good for measuring the current variability
in demand, which is useful for setting safety stock levels or estimating peak loads in a service
setting. Medium-term forecasts are useful for capturing seasonal effects, and long-term models detect general trends and are especially useful in identifying major turning points.
Which forecasting model a firm should choose depends on:
1.
2.
Time horizon to forecast
Data availability
Forecasting
ex hibit 18.3
449
Chapter 18
A Guide to Selecting an Appropriate Forecasting Method
Forecasting Method
Amount of Historical Data
Data Pattern
Forecast Horizon
Simple moving average
6 to 12 months; weekly data are
often used
Stationary only (i.e., no trend or
seasonality)
Short
Weighted moving average and
simple exponential smoothing
5 to 10 observations needed to start
Stationary only
Short
Exponential smoothing with trend
5 to 10 observations needed to start
Stationary and trend
Short
Linear regression
10 to 20 observations
Stationary, trend, and seasonality
Short to medium
Trend and seasonal models
2 to 3 observations per season
Stationary, trend, and seasonality
Short to medium
3.
4.
5.
Accuracy required
Size of forecasting budget
Availability of qualified personnel
In selecting a forecasting model, there are other issues such as the firm’s degree of flexibility.
(The greater the ability to react quickly to changes, the less accurate the forecast needs to be.)
Another item is the consequence of a bad forecast. If a large capital investment decision is to
be based on a forecast, it should be a good forecast.
S i m p l e M o v i n g A v e r a g e When demand for a product is neither growing nor
declining rapidly, and if it does not have seasonal characteristics, a moving average can be
useful in removing the random fluctuations for forecasting. The idea here is to simply
calculate the average demand over the most recent periods. Each time a new forecast is
made, the oldest period is discarded in the average and the newest period included. Thus, if
we want to forecast June with a five-month moving average, we can take the average of
January, February, March, April, and May. When June passes, the forecast for July would be
the average of February, March, April, May, and June. An example using weekly demand is
shown in Exhibit 18.4. Here, 3-week and 9-week moving average forecasts are calculated.
Notice how the forecast is shown in the period following the data used. The 3-week moving
average for week 4 uses actual demand from weeks 1, 2, and 3.
Selecting the period length should be dependent on how the forecast is going to be used.
For example, in the case of a medium-term forecast of demand for planning a budget, monthly
time periods might be more appropriate, whereas if the forecast were being used for a shortterm decision related to replenishing inventory, a weekly forecast might be more appropriate.
Although it is important to select the best period for the moving average, the number of periods to use in the forecast can also have a major impact on the accuracy of the forecast. As the
moving average period becomes shorter, and fewer periods are used, and there is more oscillation, there is a closer following of the trend. Conversely, a longer time span gives a smoother
response, but lags the trend.
The formula for a simple moving average is
​A​ ​+ ​At−2
​ ​+ ​At−3
​ ​+ . . . + ​At−n
​ ​
​​F​​= __________________
​ t−1
​​​​
t
n
​[18.1]​​
where
​ t​​ = Forecast for the coming period
F
n = Number of periods to be averaged
​
​
​ ​ ​
​At−1
​ ​ = Actual occurrence in the past period
​
​At−2
​ ​, ​At−3
​ ​, and ​At−n
​ ​ = Actual occurrences two periods ago, three periods ago, and so on,
up to n periods ago
Moving Average
A forecast based on
average past demand.
450
Supply and Demand Planning and Control
Section 4
Forecast Demand Based on a Three- and a Nine-Week Simple Moving
Average
exhibit 18.4
Week
Demand
3 Week
1
800
2
1,400
3
1,000
4
1,500
1,067
5
1,500
1,300
6
1,300
1,333
7
1,800
1,433
8
1,700
1,533
9 Week
9
1,300
1,600
10
1,700
1,600
1,367
11
1,700
1,567
1,467
12
1,500
1,567
1,500
13
2,300
1,633
1,556
14
2,300
1,833
1,644
15
2,000
2,033
1,733
16
1,700
2,200
1,811
17
1,800
2,000
1,800
18
2,200
1,833
1,811
19
1,900
1,900
1,911
20
2,400
1,967
1,933
21
2,400
2,167
2,011
22
2,600
2,233
2,111
23
2,000
2,467
2,144
24
2,500
2,333
2,111
25
2,600
2,367
2,167
26
2,200
2,367
2,267
27
2,200
2,433
2,311
28
2,500
2,333
2,311
29
2,400
2,300
2,378
30
2,100
2,367
2,378
2,800
Actual
3 week
2,400
2,000
9 week
1,600
1,200
800
400
4
8
12
16
20
24
28
32
Forecasting
Chapter 18
451
A plot of the data in Exhibit 18.4 shows the effects of using different numbers of periods in
the moving average. We see that the growth trend levels off at about the 23rd week. The threeweek moving average responds better in following this change than the nine-week average,
although overall, the nine-week average is smoother.
The main disadvantage in calculating a moving average is that all individual elements must
be carried as data because a new forecast period involves adding new data and dropping the
earliest data. For a three- or six-period moving average, this is not too severe. But plotting a
60-day moving average for the usage of each of 100,000 items in inventory would involve a
significant amount of data.
W e i g h t e d M o v i n g A v e r a g e Whereas the simple moving average assigns equal
importance to each component of the moving average database, a weighted moving average
allows any weights to be placed on each element, provided, of course, that the sum of all
weights equals 1. For example, a department store may find that, in a four-month period, the
best forecast is derived by using 40 percent of the actual sales for the most recent month,
30 percent of two months ago, 20 percent of three months ago, and 10 percent of four months
ago. If actual sales experience was
Month 1
Month 2
Month 3
Month 4
Month 5
100
90
105
95
?
A forecast made with
past data where more
recent data is given more
significance than older
data.
the forecast for month 5 would be
​ 5​​ ​= 0.40​(​95​)​+ 0.30​(​105​)​+ 0.20​(​90​)​+ 0.10​(​100​)​
F
​
​
​
​ ​ = 38 + 31.5 + 18 + 10​
​ = 97.5
The formula for a weighted moving average is
​ ​+ ​w2​​​At−2
​ ​+ . . . +​w​n​​At−n
​ ​​​
​Ft​​= ​w1​​​At−1
Weighted moving
average
​[18.2]​​
where
​w1​​ = Weight to be given to the actual occurrence for the period t − 1
​w2​​ = Weight to be given to the actual occurrence for the period t − 2
​
​
​
​wn​​ = Weight to be given to the actual occurrence for the period t − n
n = Total number of prior periods in the forecast
Although many periods may be ignored (that is, their weights are zero) and the weighting
scheme may be in any order (for example, more distant data may have greater weights than
more recent data), the sum of all the weights must equal 1.
n
​∑​​wi​​= 1​
i=1
Suppose sales for month 5 actually turned out to be 110. Then, the forecast for month 6
would be
​ 6​​ ​= 0.40​(​110​)​+ 0.30​(​95​)​+ 0.20​(​105​)​+ 0.10​(​90​)​
F
​ ​​
​ = 44 + 28.5 + 21 + 9​
​
​ = 102.5
Experience and trial and error are the simplest ways to choose weights. As a general rule, the
most recent past is the most important indicator of what to expect in the future, and, therefore, it should get higher weighting. The past month’s revenue or plant capacity, for example,
would be a better estimate for the coming month than the revenue or plant capacity of several
months ago.
However, if the data are seasonal, for example, weights should be established accordingly.
Bathing suit sales in July of last year should be weighted more heavily than bathing suit sales
in December (in the Northern Hemisphere).
452
Supply and Demand Planning and Control
Section 4
The weighted moving average has a definite advantage over the simple moving average in
being able to vary the effects of past data. However, it is more inconvenient and costly to use
than the exponential smoothing method, which we examine next.
Exponential smoothing
A time series forecasting
technique using
weights that decrease
exponentially (1 – α) for
each past period.
E x p o n e n t i a l S m o o t h i n g In the previous methods of forecasting (simple and
weighted moving averages), the major drawback is the need to continually carry a large
amount of historical data. (This is also true for regression analysis techniques, which we soon
will cover.) As each new piece of data is added in these methods, the oldest observation is
dropped and the new forecast is calculated. In many applications (perhaps in most), the most
recent occurrences are more indicative of the future than those in the more distant past. If this
premise is valid—that the importance of data diminishes as the past becomes more distant—
then exponential smoothing may be the most logical and easiest method to use.
Exponential smoothing is the most used of all forecasting techniques. It is an integral part
of virtually all computerized forecasting programs, and it is widely used in ordering inventory
in retail firms, wholesale companies, and service agencies.
Exponential smoothing techniques have become well accepted for six major reasons:
1.
2.
3.
4.
5.
6.
Smoothing constant
alpha (α)
The parameter in the
exponential smoothing
equation that controls
the speed of reaction
to differences between
forecasts and actual
demand.
Exponential models are surprisingly accurate.
Formulating an exponential model is relatively easy.
The user can understand how the model works.
Little computation is required to use the model.
Computer storage requirements are small because of the limited use of historical
data.
Tests for accuracy as to how well the model is performing are easy to compute.
In the exponential smoothing method, only three pieces of data are needed to forecast the
future: the most recent forecast, the actual demand that occurred for that forecast period, and
a smoothing constant alpha (α). This smoothing constant determines the level of smoothing
and the speed of reaction to differences between forecasts and actual occurrences. The value
for the constant is determined both by the nature of the product and by the manager’s sense of
what constitutes a good response rate. For example, if a firm produced a standard item with
relatively stable demand, the reaction rate to differences between actual and forecast demand
would tend to be small, perhaps just 5 or 10 percentage points. However, if the firm were
experiencing growth, it would be desirable to have a higher reaction rate, perhaps 15 to 30
percentage points, to give greater importance to recent growth experience. The more rapid the
growth, the higher the reaction rate should be. Sometimes users of the simple moving average
switch to exponential smoothing but like to keep the forecasts about the same as the simple
moving average. In this case, α is approximated by 2 ÷ (n + 1), where n is the number of time
periods in the corresponding simple moving average.
The equation for a single exponential smoothing forecast is simply
​ ​+ α(​At−1
​ ​− ​Ft−1
​ ​)​
​Ft​​= ​Ft−1
​[18.3]​​
where
​ t​​ = The exponentially smoothed forecast for period t
F
​Ft−1
​ ​ = The exponentially smoothed forecast made for the prior period
​
​
​
​
​
​At−1
​ ​ = The actual demand in the prior period
α = The desired response rate, or smoothing constant
This equation states that the new forecast is equal to the old forecast plus a portion of the error
(the difference between the previous forecast and what actually occurred).
To demonstrate the method, assume that the long-run demand for the product under study
is relatively stable and a smoothing constant (α) of 0.05 is considered appropriate. If the exponential smoothing method were used as a continuing policy, a forecast would have been made
Forecasting
Chapter 18
453
for last month. Assume that last month’s forecast (Ft–1) was 1,050 units. If 1,000 actually were
demanded, rather than 1,050, the forecast for this month would be
​Ft​​ ​= ​Ft−1
​ ​+ α​(​​At−1
​ ​− ​Ft−1
​ ​)​
​ ​= 1, 050 + 0.05​(​1, 000 − 1, 050​)​
​
​
​
​
​ ​= 1, 050 + 0.05​(​− 50​)​
​ = 1, 047.5 units
Because the smoothing coefficient is small, the reaction of the new forecast to an error of
50 units is to decrease the next month’s forecast by only 2½ units.
When exponential smoothing is first used for an item, an initial forecast may be obtained
by using a simple estimate, like the first period’s demand, or by using an average of preceding
periods, such as the average of the first two or three periods.
Single exponential smoothing has the shortcoming of lagging changes in demand.
Exhibit 18.5 presents actual data plotted as a smooth curve to show the lagging effects of
the exponential forecasts. The forecast lags during an increase or decrease, but overshoots
when a change in direction occurs. Note that the higher the value of alpha, the more closely
the forecast follows the actual. To more closely track actual demand, a trend factor may be
added. Adjusting the value of alpha also helps. This is termed adaptive forecasting. Both
trend effects and adaptive forecasting are briefly explained in the following sections.
E x p o n e n t i a l S m o o t h i n g w i t h T r e n d Remember that an upward or downward
trend in data collected over a sequence of time periods causes the exponential forecast to
always lag behind (be above or below) the actual occurrence. Exponentially smoothed
forecasts can be corrected somewhat by adding in a trend adjustment. To correct the trend, we
need two smoothing constants. Besides the smoothing constant α, the trend equation also uses
a smoothing constant delta (δ). Both alpha and delta reduce the impact of the error that
occurs between the actual and the forecast. If both alpha and delta are not included, the trend
overreacts to errors.
ex hibit 18.5
Exponential Forecasts versus Actual Demand for Units of a Product
over Time Showing the Forecast Lag
500
400
α = .5
Ft = Ft – 1 + α(At – 1 – Ft
α = 0.1, 0.3, and 0.5
– 1)
α = .3
300
Actual
α = .1
200
100
0
J
F M A M J
J
A S O N D
J
F M A M J
J
A S O N D
J
F
Smoothing constant
delta (δ)
An additional parameter
used in an exponential
smoothing equation that
includes an adjustment for
trend.
454
Section 4
Supply and Demand Planning and Control
To get the trend equation going, the first time it is used the trend value must be entered
manually. This initial trend value can be an educated guess or a computation based on
observed past data.
The equations to compute the forecast including trend (FIT) are​​​​​​​
Ft = FITt–1 + α(At–1 – FITt–1)
​[18.4]​​
Tt = Tt–1 + δ(Ft – FITt–1)
​[18.5]​​
FITt = Ft + Tt
​[18.6]​​
where
​Ft​​ = The exponentially smoothed forecast that does not include trend for period t
​Tt​​ = The exponentially smoothed trend for period t
​FIT​t​ = The forecast including trend for period t
​ = The forecast including trend​ made for the
​ ​ prior​ period​
​
​F
IT​
t−1
​At−1
​ ​ = The actual demand for the prior period
α = Smoothing constant (alpha)
δ = Smoothing constant (delta)
To make an exponential forecast that includes trend, step through the equations one at a time.
Step 1: Using Equation 18.4, make a forecast that is not adjusted for trend. This uses the
previous forecast and previous actual demand.
Step 2: Using Equation 18.5, update the estimate of trend using the previous trend estimate, the unadjusted forecast just made, and the previous forecast.
Step 3: Make a new forecast that includes trend by using the results from steps 1 and 2.
EXAMPLE 18.1: Forecast Including Trend
Assume a previous forecast, including a trend of 110 units, a previous trend estimate of
10 units, an alpha of .20, and a delta of .30. If actual demand turned out to be 115 rather than
the forecast 110, calculate the forecast for the next period.
SOLUTION
The actual At–1 is given as 115. Therefore,
​Ft​​ ​= ​FIT​t−1​+ α​(​​At−1
​ ​− ​FIT​t−1​)​
​ ​= 110 + .2​(​115 − 110​)​= 111.0​
​
​
​T
​
​= ​Tt−1
​ ​+ δ​(​​Ft​​− ​FIT​t−1)​ ​ ​ ​ ​ ​
t
​ ​= 10 + .3​(​111 − 110​)​= 10.3​
​FIT​t​ = ​Ft​​+ ​Tt​​= 111.0 + 10.3 = 121.3
If, instead of 121.3, the actual turned out to be 120, the sequence would be repeated and the
forecast for the next period would be
​ t+1
F
​ ​ ​= 121.3 + .2​(​120 − 121.3​)​= 121.04​
​ ​= 10.3 + .3​(​121.04 − 121.3​)​= 10.22​​​
​ ​T
t+1​
​FIT​t+1​ = 121.04 + 10.22 = 131.26
Exponential smoothing requires that the smoothing constants be given a value between 0
and 1. Typically, fairly small values are used for alpha and delta in the range of .1 to .3. The
values depend on how much random variation there is in demand and how steady the trend
factor is. Later in the chapter, error measures are discussed that can be helpful in picking
appropriate values for these parameters.
Forecasting
Chapter 18
L i n e a r R e g r e s s i o n A n a l y s i s Regression can be defined as a functional relationship
between two or more correlated variables. It is used to predict one variable given the others.
The relationship is usually developed from observed data. The data should be plotted first to
see if they appear linear or if at least parts of the data are linear. Linear regression refers to
the special class of regression where the relationship between variables forms a straight line.
The linear regression line is of the form Y = a + bt, where Y is the value of the dependent variable that we are solving for, a is the Y intercept, b is the slope, and t is an index for the time period.
Linear regression is useful for long-term forecasting of major occurrences and aggregate
planning. For example, linear regression would be very useful to forecast demands for product
families. Even though demand for individual products within a family may vary widely during
a time period, demand for the total product family is surprisingly smooth.
The major restriction in using linear regression forecasting is, as the name implies, that past
data and future projections are assumed to fall in about a straight line. Although this does limit its
application sometimes, if we use a shorter period of time, linear regression analysis can still be
used. For example, there may be short segments of the longer period that are approximately linear.
Linear regression is used both for time series forecasting and for causal relationship forecasting. When the dependent variable (usually the vertical axis on a graph) changes as a result
of time (plotted as the horizontal axis), it is time series analysis. If one variable changes
because of the change in another variable, this is a causal relationship (such as the number of
deaths from lung cancer increasing with the number of people who smoke).
We use the following example to demonstrate linear least squares regression analysis.
EXAMPLE 18.2: Least Squares Method
A firm’s sales for a product line during the 12 quarters of the past three years were as follows:
Quarter
Sales
Quarter
Sales
1
2
3
4
5
6
600
1,550
1,500
1,500
2,400
3,100
7
8
9
10
11
12
2,600
2,900
3,800
4,500
4,000
4,900
The firm wants to forecast each quarter of the fourth year—that is, quarters 13, 14, 15, and 16.
SOLUTION
The least squares equation for linear regression is
where
​Y = a + bt​
​[18.7]​​
Y = Dependent variable computed by the equation
y = The actual dependent variable data point (used as follows)
a​
​
​ = Y intercept​
​
​
​
b = Slope of the line
t = Time period
The least squares method tries to fit the line to the data that minimizes the sum of the
squares of the vertical distance between each data point and its corresponding point on the
line. If a straight line is drawn through the general area of the points, the difference between
the point and the line is y – Y. Exhibit 18.6 shows these differences. The sum of the squares of
the differences between the plotted data points and the line points is
​(​y1​​− ​Y1​​)​​2​+ ​(​y2​​− ​Y2​​)​​2​+ . . . +​(​y12
​ ​− ​Y12
​ ​)​​2​
The best line to use is the one that minimizes this total.
As before, the straight line equation is
Y = a + bt
455
Linear regression
forecasting
A forecasting technique
that fits a straight line to
past demand data.
456
Section 4
Supply and Demand Planning and Control
exhibit 18.6
Least Squares Regression Line
$5,000
4,500
y10
y9
4,000
Y8
3,500
y6
3,000
Sales
y5
2,500
2,000
y2
1,500
1,000
Y1
500
y1
0
Y2
1
2
y3
Y3
3
Y6
Y7
y12
Y11
Y12
Y10 y11
Y9
y8
y7
Y5
Y4
y4
4
6
5
7
8
9
10
11
12
Quarters
In the least squares method, the equations for a and b are
∑ t ​y​ − n​ ¯t​ · y ​
​​  ¯​  ​​
b = ​​ ___________
​​
2
2
∑ ​t​ ​ − n ¯​​ t​​​  ​
​[18.8]​​
​  ¯ − b​ ¯t​​​​
​​a = y ​
​[18.9]​​
where
a = Y intercept
b = Slope of the line
y​¯​ = Average of all ys
t​¯​ = Average of all ts
​
​
​
​​
​ ​​
​
t = t value at each data point
y = y value at each data point
n = Number of data points
Y = Value of the dependent variable computed with the regression equation
Exhibit 18.7 shows these computations carried out for the 12 data points in the problem. Note
that the final equation for Y shows an intercept of 441.67 and a slope of 359.6. The slope
shows that for every unit change in t, Y changes by 359.6. Note that these calculations can be
done with the INTERCEPT and SLOPE functions in Microsoft Excel.
Strictly based on the equation, forecasts for periods 13 through 16 would be
​ 13
Y
​ ​= 441.67 + 359.6​(​13​)​= 5,116.5
​Y14
​ ​​= 441.67 + 359.6​(​14​)​= 5,476.1
​ ​
​
​
​Y15
​ ​​= 441.67 + 359.6​(​15​)​= 5,835.7
​Y16
​ ​​= 441.67 + 359.6​(​16​)​= 6,195.3
The standard error of estimate, or how well the line fits the data, is
√
__________
n
​∑​​(​yi​​− ​Yi​​)​​2​
​​
​​​​
__________
​Syt​ ​= ​ ​  i=1
​ ​
n−2
​[18.10]​​
Forecasting
exhibit 18.7
(1)
t
(2)
y
Chapter 18
Least Squares Regression Analysis
(3)
t×y
1
600
600
2
1,550
3,100
3
1,500
4,500
4
1,500
6,000
5
2,400
12,000
6
3,100
18,600
7
2,600
18,200
8
2,900
23,200
9
3,800
34,200
10
4,500
45,000
11
4,000
44,000
12
4,900
58,800
78
33,350
268,200
¯t​
​​  = 6.5 b = 359.6154​
¯
​​  = 2, 779.17 a = 441.6667​
y​
​Therefore, Y = 441.67 + 359.6t​
​S​yt​= 363.9​
(4)
t2
(5)
y2
(6)
y
1
4
9
16
25
36
49
64
81
100
121
144
650
360,000
2,402,500
2,250,000
2,250,000
5,760,000
9,610,000
6,760,000
8,410,000
14,440,000
20,250,000
16,000,000
24,010,000
112,502,500
801.3
1,160.9
1,520.5
1,880.1
2,239.7
2,599.4
2,959.0
3,318.6
3,678.2
4,037.8
4,397.4
4,757.1
The standard error of estimate is computed from the second and last columns of Exhibit 18.7:
_____________________________________________________________________
(​ ​600 − 801.3​)​2​+ (​ ​1, 550 − 1, 160.9​)​2​+ (​ ​1, 500 − 1, 520.5​)​2​+ . . . + (​ ​4, 900 − 4, 757.1​)​2​
_____________________________________________________________________
​S​​
​
​ ​​​​
​ yt​ ​​  = ​
10
​ = 363.9
√
In addition to the INTERCEPT and SLOPE functions, Microsoft Excel has a very powerful
regression tool designed to perform these calculations. (Note that it can also be used for moving average and exponential smoothing calculations.) To use the tool, a table is needed that
contains data relevant to the problem (see Exhibit 18.8). The tool is part of the Data Analysis
exhibit 18.8
Excel Regression Tool
457
458
Supply and Demand Planning and Control
Section 4
ToolPak that is accessed from the Data menu (you may need to add this to your Data options
by using the Add-In option under File → Options → Add-Ins).
To use the tool, first input the data in two columns in your spreadsheet, then access the
Regression option from the → Data menu. Next, specify the Y Range, which is B2:B13, and
the time periods in the X Range, which is A2:A13 in our example. Finally, an Output Range
is specified. This is where you would like the results of the regression analysis placed in your
spreadsheet. In the example, A16 is entered. There is some information provided that goes
beyond what we have covered, but what you are looking for is the Intercept and X Variable
coefficients that correspond to the intercept and slope values in the linear equation. These are
in cells B32 and B33 in Exhibit 18.8.
Decomposition
The process of identifying
and separating time series
data into fundamental
components such as trend
and seasonality.
D e c o m p o s i t i o n o f a T i m e S e r i e s A time series can be defined as chronologically
ordered data that may contain one or more components of demand: trend, seasonal, cyclical,
autocorrelation, and random. Decomposition of a time series means identifying and separating
the time series data into these components. In practice, it is relatively easy to identify the
trend (even without mathematical analysis, it is usually easy to plot and see the direction of
movement) and the seasonal component (by comparing the same period year to year). It is
considerably more difficult to identify the cycles (these may be many months or years long), the
autocorrelation, and the random components. (The forecaster usually calls random anything left
over that cannot be identified as another component.)
When demand contains both seasonal and trend effects at the same time, the question is
how they relate to each other. In this description, we examine two types of seasonal variation:
additive and multiplicative.
Additive seasonal variation simply assumes that the seasonal amount is a constant no matter what the trend or average amount is.
Forecast including trend and seasonal = Trend + Seasonal
Exhibit 18.9A shows an example of increasing trend with constant seasonal amounts.
In multiplicative seasonal variation, the trend is multiplied by the seasonal factors.
Forecast including trend and seasonal = Trend × Seasonal factor
Exhibit 18.9B shows the seasonal variation increasing as the trend increases because its
size depends on the trend.
The multiplicative seasonal variation is the usual experience. Essentially, this says that the
larger the basic amount projected, the larger the variation around this that we can expect.
A seasonal factor is the amount of correction needed in a time series to adjust for the season of the year.
exhibit 18.9
Additive and Multiplicative Seasonal Variation Superimposed on Changing Trend
January
Amount
B. Multiplicative Seasonal
Amount
A. Additive Seasonal
July
January
July
January
July
January
July
January
January
July
January
July
January
July
January
July
January
Forecasting
Chapter 18
459
Companies such as
Toro manufacture
lawnmowers and snow
blowers to match
seasonal demand. Using
the same equipment
and assembly lines
provides better capacity
utilization, workforce
stability, productivity,
and revenue.
Courtesy of The Toro
Company
We usually associate seasonal with a period of the year characterized by some particular activity. We use the word cyclical to indicate other than annual recurrent periods of repetitive activity.
The following examples show how seasonal indexes are determined and used to forecast
(1) a simple calculation based on past seasonal data and (2) the trend and seasonal index from
a hand-fit regression line. We follow this with a more formal procedure for the decomposition
of data and forecasting using least squares regression.
EXAMPLE 18.3: Simple Proportion
Assume that in past years, a firm sold an average of 1,000 units of a particular product line
each year. On the average, 200 units were sold in the spring, 350 in the summer, 300 in the
fall, and 150 in the winter. The seasonal factor (or index) is the ratio of the amount sold during
each season divided by the average for all seasons.
SOLUTION
In this example, the yearly amount divided equally over all seasons is 1,000 ÷ 4 = 250. The
seasonal factors therefore are
Past
Sales
Average Sales
for Each Season
(1,000/4)
Seasonal
Factor
Spring
200
250
200/250 = 0.8
Summer
350
250
350/250 = 1.4
Fall
300
250
300/250 = 1.2
Winter
150
250
150/250 = 0.6
Total
1,000
Using these factors, if we expected demand for next year to be 1,100 units, we would forecast
the demand to occur as
Expected
Demand for
Next Year
Average
Sales for
Each Season
(1,100/4)
Next Year’s
Seasonal
Forecast
Seasonal
Factor
Spring
275
×
0.8
=
220
Summer
275
×
1.4
=
385
Fall
275
×
1.2
=
330
275
×
0.6
=
165
Winter
_____
Total
1,100
460
Section 4
Supply and Demand Planning and Control
The seasonal factor may be periodically updated as new data are available. The following
example shows the seasonal factor and multiplicative seasonal variation.
EXAMPLE 18.4: Computing Trend and Seasonal Factor from a Linear Regression
Line Obtained with Excel
Forecast the demand for each quarter of the next year using trend and seasonal factors.
Demand for the past two years is in the following table:
Quarter
Amount
Quarter
Amount
1
300
5
520
2
200
6
420
3
220
7
400
4
530
8
700
SOLUTION
First, we plot as in Exhibit 18.10 and then calculate the slope and intercept using Excel. For
Excel, the quarters are numbered 1 through 8. The “known ys” are the amounts (300, 200,
220, etc.), and the “known xs” are the quarter numbers (1, 2, 3, etc.). We obtain a slope = 52.3
(rounded), and intercept = 176.1 (rounded). The equation for the line is
Forecast Including Trend (FIT) = 176.1 + 52.3t
Computing a Seasonal Factor from the Actual Data and Trend Line
exhibit 18.10
700
600
500
400
300
200
100
I
II
III
IV
I
2011
Quarter
Actual
amount
II
III
From trend
equation
FITt = 176.1 + 52.3t
Ratio of
actual ÷ trend
228.3
280.6
332.9
385.1
—
437.4
489.6
541.9
594.2
1.31
0.71
0.66
1.38
—
1.19
0.86
0.74
1.18
Seasonal factor
(average of same
quarters in both years)
2011
I
II
III
IV
2012
I
II
III
IV
300
200
220
530
520
420
400
700
IV
2012
I 1.25
II 0.79
III 0.70
IV 1.28
Forecasting
461
Chapter 18
Next, we can derive a seasonal index by comparing the actual data with the trend line, as in
Exhibit 18.10. The seasonal factor was developed by averaging the same quarters in each year.
We can compute the 2013 forecast including trend and seasonal factors (FITS) as follows:
​ ITS​t​ = FIT × Seasonal
F
I—2013 ​FITS​9​ ​= ​[​176.1 + 52.3​(​9​)​]​1.25 = 808​
II—2013
​FITS​10​ ​= [​ ​176.1 + 52.3​(​1​0​)]​ ​0.79 = 552​
​
​​ ​
III—2013 ​FITS​11​ ​= [​ ​176.1 + 52.3​(​11​)]​ ​0.70 = 526​
IV—2013 ​FITS​12​ ​= [​ ​176.1 + 52.3​(​12​)]​ ​1.28 = 1, 029​
Note, these numbers were calculated using Excel, so your numbers may differ slightly due to
rounding.
D e c o m p o s i t i o n U s i n g L e a s t S q u a r e s R e g r e s s i o n This procedure is
different from the previous one and in some cases may give better results. The approach
described in Example 18.3 started by fitting a regression line, and given the line, the seasonal
indexes are calculated. With this approach, we start by calculating seasonal indexes. Then,
using data that have been “deseasonalized,” we estimate a trend line using linear regression.
More formally, the process is:
1.
Decompose the time series into its components.
a. Find seasonal component.
b. Deseasonalize the demand.
c. Find trend component.
ex hibit 18.11
(1)
(2)
Period
(t)
Quarter
Deseasonalized Demand
(3)
Actual
Demand
(y)
(4)
(5)
(6)
Deseasonalized
Demand (yd)
Col. (3) ÷ Col. (5)
(7)
Average of the Same
Quarters of Each Year
Seasonal
Factor
(600 + 2,400 + 3,800)∕3
= 2,266.7
0.82
735.7
1
735.7
t2
(Col. 1)2
(8)
t × yd
Col. (1) ×
Col. (6)
1
I
600
2
II
1,550
(1,550 + 3,100 + 4,500)∕3
= 3,050
1.10
1,412.4
4
2,824.7
3
III
1,500
(1,500 + 2,600 + 4,000)∕3
= 2,700
0.97
1,544.0
9
4,631.9
4
IV
1,500
(1,500 + 2,900 + 4,900)∕3
= 3,100
1.12
1,344.8
16
5,379.0
5
I
2,400
0.82
2,942.6
25
14,713.2
6
II
3,100
1.10
2,824.7
36
16,948.4
7
III
2,600
0.97
2,676.2
49
18,733.6
8
IV
2,900
1.12
2,599.9
64
20,798.9
9
I
3,800
0.82
4,659.2
81
41,932.7
10
II
4,500
1.10
4,100.4
100
41,004.1
11
III
4,000
0.97
4,117.3
121
45,290.1
12
IV
4,900
1.12
4,392.9
144
52,714.5
33,350*
12.03
33,350.1*
650
265,706.9
78
∑ t y​ ​​​ − n¯t​ ​y​ d​​​ 265, 706.9 − 12(​ ​6
​ .5)​ ​2​ , 779.2
¯​t​ ​= ___
​78
​= 6.5b = _________
​  2d
​= __________________________
​
​= 342.2​
12
∑ t​​ ​ − n ¯t​​​2​
650 − 12 (​ ​6
​ .5)​ ​​2​
¯
y​​​  d​​  ​​ = 33, 350 / 12 = 2, 779.2a = ¯
y​​  d​​  ​​ − b¯​t ​= 2, 779.2 − 342.2​(​​6.5​)​​= 554.9​
​Therefore,Y = a + bt = 554.9 + 342.2t​
*Column 3 and column 6 totals should be equal at 33,350. Differences are due to rounding. Column 5 was rounded to two decimal places.
462
Supply and Demand Planning and Control
Section 4
2.
Forecast future values of each component.
a. Project trend component into the future.
b. Multiply trend component by seasonal component.
Exhibit 18.11 shows the decomposition of a time series using least squares regression and
the same basic data we used in our first regression example. Each data point corresponds to
using a single three-month quarter of the three-year (12-quarter) period. Our objective is to
forecast demand for the four quarters of the fourth year.
Step 1. Determine the seasonal factor (or index). Exhibit 18.11 summarizes the calculations needed. Column 4 develops an average for the same quarters in the three-year period.
For example, the first quarters of the three years are added together and divided by three.
A seasonal factor is then derived by dividing that average by the general average for all
⎛ 33, 350
⎞
2, 266.7
12 quarters ​​​ ______
​​
​
, or 2,779​ ​​​. For example, this first quarter seasonal factor is _______
​​
​ =
⎝ 12
⎠
2, 779
0.82​. These are entered in column 5. Note that the seasonal factors are identical for similar
quarters in each year.
⎜
⎟
Step 2. Deseasonalize the original data. To remove the seasonal effect on the data, we
divide the original data by the seasonal factor. This step is called the deseasonalization of
demand and is shown in column 6 of Exhibit 18.11.
Step 3. Develop a least squares regression line for the deseasonalized data. The purpose here is to develop an equation for the trend line Y, which we then modify with the
seasonal factor. The procedure is the same as we used before:
Y = a + bt
where
yd
t
Y
a
b
=
=
=
=
=
Deseasonalized demand (see Exhibit 18.11)
Quarter
Demand computed using the regression equation Y = a + bt
Y intercept
Slope of the line
The least squares calculations using columns 1, 7, and 8 of Exhibit 18.11 are shown in the
lower section of the exhibit. The final deseasonalized equation for our data is Y = 554.9 +
342.2t. This straight line is shown in Exhibit 18.12.
exhibit 18.12
Straight Line Graph of Deseasonalized Equation
5,000
4,500
4,000
3,500
3,000
Sales 2,500
2,000
1,500
1,000
500
0
Deseasonalized equation
Y = 554.9 + 342.2 x
Original data
Deseasonalized data
1
2
3
4
5
6
7
Quarters
8
9 10 11 12
Forecasting
Chapter 18
463
Step 4. Project the regression line through the period to be forecast. Our purpose is
to forecast periods 13 through 16. We start by solving the equation for Y at each of these
periods (shown in step 5, column 3).
Step 5. Create the final forecast by adjusting the regression line by the seasonal factor. Recall that the Y equation has been deseasonalized. We now reverse the procedure by multiplying the quarterly data we derived by the seasonal factor for that quarter:
Period
Quarter
Y from
Regression Line
Seasonal Factor
Forecast
(Y × Seasonal Factor)
13
1
5,003.5
0.82
4,102.87
14
2
5,345.7
1.10
5,880.27
15
3
5,687.9
0.97
5,517.26
16
4
6,030.1
1.12
6,753.71
Our forecast is now complete.
When a straight line is fitted through data points and then used for forecasting, errors can
come from two sources. First, there are the usual errors similar to the standard deviation of
any set of data. Second, there are errors that arise because the line is wrong. Exhibit 18.13
shows this error range. Instead of developing the statistics here, we will briefly show why the
range broadens. First, visualize that one line is drawn that has some error such that it slants
too steeply upward. Standard errors are then calculated for this line. Now visualize another
line that slants too steeply downward. It also has a standard error. The total error range, for
this analysis, consists of errors resulting from both lines, as well as all other possible lines.
We included this exhibit to show how the error range widens as we go further into the future.
For e ca s t Er r or s
In using the term forecast error, we are referring to the difference between what actually
occurred and what was forecast. In statistics, these errors are called residuals. As long as
the forecast value is within the confidence limits, as we discuss later under the heading,
“­Measurement of Error,” this is not really an error because it is what we expected. But common usage refers to the difference as an error.
Demand for a product is generated through the interaction of a number of factors too complex to describe accurately in a model. Therefore, all forecasts certainly contain some error.
In discussing forecast errors, it is convenient to distinguish between sources of error and the
measurement of error.
Sources of Error Errors can come from a variety of sources. One common source that many
forecasters are unaware of is projecting past trends into the future. For example, when we talk
ex hibit 18.13
Prediction Intervals for Linear Trend
Prediction
interval
Demand
Prediction
interval
Past
nt
pone
om
nd c
Tre
Present
Time
Future
Forecast error
The difference between
actual demand and what
was forecast.
464
Section 4
Supply and Demand Planning and Control
about statistical errors in regression analysis, we are referring to the deviations of observations
from our regression line. It is common to attach a confidence band (that is, statistical control
limits) to the regression line to reduce the unexplained error. But when we then use this
regression line as a forecasting device by projecting it into the future, the error may not be
correctly defined by the projected confidence band. This is because the confidence interval is
based on past data; it may not hold for projected data points and therefore cannot be used with
the same confidence. In fact, experience has shown that the actual errors tend to be greater
than those predicted from forecast models.
Errors can be classified as bias or random. Bias errors occur when a consistent mistake is
made. Sources of bias include the failure to include the right variables; the use of the wrong
relationships among variables; employing the wrong trend line; a mistaken shift in the seasonal demand from where it normally occurs; and the existence of some undetected secular
trend. R
­ andom errors can be defined as those that cannot be explained by the forecast model
being used.
Mean absolute
deviation (MAD)
The average of the
absolute value of the
actual forecast error.
M e a s u r e m e n t o f E r r o r Several common terms used to describe the degree of
error are standard error, mean squared error (or variance), and mean absolute deviation. In
addition, tracking signals may be used to indicate any positive or negative bias in the forecast.
Standard error is discussed in the section on linear regression in this chapter. Because the
standard error is the square root of a function, it is often more convenient to use the function
itself. This is called the mean squared error, or variance.
The mean absolute deviation (MAD) was in vogue in the past but subsequently was
ignored in favor of standard deviation and standard error measures. In recent years, MAD has
made a comeback because of its simplicity and usefulness in obtaining tracking signals.
MAD is the average error in the forecasts, using absolute values. It is valuable because MAD,
like the standard deviation, measures the dispersion of some observed value from some
expected value.
MAD is computed using the differences between the actual demand and the forecast
demand without regard to sign. It equals the sum of the absolute deviations divided by the
number of data points or, stated in equation form,
n
|
|
​ ​​​At​​− ​Ft​​​
∑
​
​​​​
________
MAD = ​t=1 n
​
​[18.11]​​
where
t = Period number
​ t​​​ = Actual demand for the period t
A
​F
​​​ = Forecast demand
​ for the​period​ t​
​
t​​ ​​
n = Total number of periods
∥ = A symbol used to indicate the absolute value disregarding positive and negative signs
When the errors that occur in the forecast are normally distributed (the usual case), the
mean absolute deviation relates to the standard deviation of the error terms as
__
π ​ ​ × MAD, or approximately 1.25 MAD​​
__
​
​​1 standard deviation ≈ ​√
2
Conversely,
1 MAD is approximately 0.8 standard deviation
The standard deviation is the larger measure. If the MAD of a set of points was found to be
60 units, then the standard deviation would be approximately 75 units. In the usual statistical
manner, if control limits were set at plus or minus 3 standard deviations (or ±3.75 MADs),
then 99.7 percent of the points would fall within these limits.
Forecasting
Chapter 18
465
An additional measure of error that is often useful is the mean absolute percent error Mean absolute percent
(MAPE). This measure gauges the error relative to the demand as a percentage. For example, error (MAPE)
if the error is 10 units and actual demand is 20 units, the error is 50 percent The average error
measured as a percentage
⎛___
⎞
​​​⎝​​  10 ​ = .50​⎠​​​. In the case of an average demand of 1,000 units, the MAPE would be only 1 percent of average demand.
20
⎛_____
⎞
​ ​​  10  ​ = .01​ ​​​. MAPE is the average of the percent error. MAPE is calculated as follows:
⎝ 1,000
⎠
⎡ ​​At​​– ​Ft​​ ​⎤
n ⎢_____
⎥
​[18.12]​​
​MAPE ​= ___
​100
n ​​∑ t=1 ​⎣​ ​A​​ ​⎦​​​​
⎜
⎟
|
|
t
This is a useful measure because it is an estimate of how much error to expect with a forecast. The real value of the MAPE is that it allows you to compare forecasts between ­products
that have very different average demand. If you used the MAD, the product with the higher
demand would have the higher MAD even if it was a better forecast.
A tracking signal is a measurement that indicates whether the forecast average is keeping
pace with any genuine upward or downward changes in demand. When a forecast is consistently low or high, it is referred to as a biased forecast. Exhibit 18.14 shows a normal distribution with a mean of 0 and a MAD equal to 1. Thus, if we compute the tracking signal and find
it equal to minus 2, we can see that the forecast model is providing forecasts that are quite a
bit above the mean of the actual occurrences.
A tracking signal (TS) can be calculated using the arithmetic sum of forecast deviations
divided by the mean absolute deviation:
​TS = _____
​RSFE ​​​
MAD
​[18.13]​​
where​​
RSFE = The running sum of forecast errors, considering the nature of the error. (For
­example, negative errors cancel positive errors and vice versa.)
MAD = The average of all the forecast errors (disregarding whether the deviations are
positive or negative). It is the average of the absolute deviations.
Exhibit 18.15 illustrates the procedure for computing MAD and the tracking signal for a sixmonth period where the forecast had been set at a constant 1,000 and the actual demands that
occurred are as shown. In this example, the forecast, on the average, was off by 66.7 units and
the tracking signal was equal to 3.3 mean absolute deviations.
A Normal Distribution with Mean = 0 and MAD = 1
ex hibit 18.14
−4 MAD
4 MAD
−3 MAD
3 MAD
−2 MAD
2 MAD
−1 MAD
4
3
2
1
1 MAD
Mean = 0
1
2
3
4
Tracking signal
A measure of whether the
forecast is keeping pace
with any genuine upward
or downward changes in
demand. This is used to
detect forecast bias.
466
Supply and Demand Planning and Control
Section 4
exhibit 18.15
Computing the Mean Absolute Deviation (MAD), the Running
Sum of Forecast Errors (RSFE), and the Tracking Signal (TS) from
Forecast and Actual Data
Month
Demand
Forecast
Abs. Dev.
Sum of
Abs. Dev.
1
1,000
950
−50
−50
50
50
50 (5.26%)
2
1,000
1,070
+70
+20
70
120
60 (5.61%)
3
1,000
4
1,000
1,100
+100
+120
100
220
73.3 (6.67%)
960
−40
180
40
260
65 (6.77%)
1.2
5
6
1,000
1,090
+90
+170
90
350
70 (6.42%)
2.4
1,000
1,050
+50
+220
50
400
66.7 (6.35%)
3.3
Actual
Deviation
RSFE
MAD
(% Error)*
RSFE†
​TS = _____
​
​​
MAD
−1
.33
1.64
*Overall, MAD = 400 ÷ 6 = 66.7. MAPE = (5.26 + 5.61 + 6.67 + 6.77 + 6.42 + 6.35)/6 = 6.18%
RSFE ____
220
†Overall, T
​ S = _____
​
​ = ​
​ = 3.3 MADs​.
MAD 66.7
4
3
Actual
exceeds
forecast
2
Tracking 1
signal
0
Actual is
less than
forecast
−1
−2
−3
1
2
3
4
5
6
Month
We can get a better feel for what the MAD and tracking signal mean by plotting the points
on a graph. Though this is not completely legitimate from a sample-size standpoint, we plotted each month in Exhibit 18.15 to show the drift of the tracking signal. Note that it drifted
from minus 1 MAD to plus 3.3 MADs. This happened because actual demand was greater
than the forecast in four of the six periods. If the actual demand does not fall below the forecast to offset the continual positive RSFE, the tracking signal would continue to rise and we
would conclude that assuming a demand of 1,000 is a bad forecast.
Ca us a l Re la tio n sh ip F o recast in g
Causal relationship
forecasting
Forecasting using
independent variables
other than time to predict
future demand.
Causal relationship forecasting involves using independent variables other than time to predict future demand. To be of value for the purpose of forecasting, any independent variable
must be a leading indicator. For example, we can expect that an extended period of rain will
increase sales of umbrellas and raincoats. The rain causes the sale of rain gear. This is a causal
relationship, where one occurrence causes another. If the causing element is known far enough
in advance, it can be used as a basis for forecasting.
Often, leading indicators are not causal relationships, but in some indirect way they
may suggest that some other things might happen. Other noncausal relationships just seem
to exist as a coincidence. The following shows one example of a forecast using a causal
relationship.
Forecasting
Chapter 18
EXAMPLE 18.5: Forecasting Using a Causal Relationship
The Carpet City Store in Carpenteria has kept records of its sales (in square yards) each year,
along with the number of permits for new houses in its area.
Number of Housing Starts
Year
Permits
Sales
(in Sq. Yds.)
1
18
13,000
2
15
12,000
3
12
11,000
4
10
10,000
5
20
14,000
6
28
16,000
7
35
19,000
8
30
17,000
9
20
13,000
Carpet City’s operations manager believes forecasting sales is possible if housing starts are
known for that year. First, the data are plotted in Exhibit 18.16, with
x = Number of housing start permits
y = Sales of carpeting
Because the points appear to be in a straight line, the manager decides to use the linear
relationship Y = a + bx.
SOLUTION
An easy way to solve this problem is to use the SLOPE and INTERCEPT functions in Excel.
Given the data in the table, the SLOPE is equal to 344.2211 and the INTERCEPT is equal to
6698.492.
ex hibit 18.16
Causal Relationship: Sales to Housing Starts
Y 20,000
18,000
16,000
14,000
Y
12,000
Sales
(square
10,000
yards of
carpet)
8,000
X
6,000
4,000
2,000
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Number of housing start permits
X
467
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Section 4
Supply and Demand Planning and Control
The manager interprets the slope as the average number of square yards of carpet sold for
each new house built in the area. The forecasting equation is therefore
Y = 6698.492 + 344.2211x
Now suppose that there are 25 permits for houses to be built next year. The sales forecast
would therefore be
6,698.492 + 344.2211(25) = 15,304.02 square yards
In this problem, the lag between filing the permit with the appropriate agency and the new
home owner coming to Carpet City to buy carpet makes a causal relationship feasible for
forecasting.
M u l t i p l e R e g r e s s i o n A n a l y s i s Another forecasting method is multiple
regression analysis, in which a number of variables are considered, together with the effects
of each on the item of interest. For example, in the home furnishings field, the effects of the
number of marriages, housing starts, disposable income, and the trend can be expressed in a
multiple regression equation as
S = A + Bm(M) + Bh(H) + Bi(I) + Bt(T)
where
S = Gross sales for year
A = Base sales, a starting point from which other factors have influence
M = Marriages during the year
​
​
​
​ ​
​
​
H = Housing starts during the year
I = Annual disposable personal income
T = Time trend (first year = 1, second = 2, third = 3, and so forth)
Bm, Bh, Bi, and Bt represent the influence on expected sales of the numbers of marriages and
housing starts, income, and trend.
Forecasting by multiple regression is appropriate when a number of factors influence a
variable of interest—in this case, sales. Its difficulty lies with collecting all the additional data
that is required to produce the forecast, especially data that comes from outside the firm. Fortunately, standard computer programs for multiple regression analysis are available, relieving
the need for tedious manual calculation.
Microsoft Excel supports the time series analysis techniques described in this section.
These functions are available under the Data Analysis tools for exponential smoothing, moving averages, and regression.
QUALI TATIVE TECHNIQ UES IN FORECASTING
LO 18–3
Apply qualitative
techniques to forecast
demand.
Qualitative forecasting techniques generally take advantage of the knowledge of experts and
require much judgment. These techniques typically involve processes that are well defined
to those participating in the forecasting exercise. For example, in the case of forecasting the
demand for new fashion merchandise in a retail store, the firm can include a combination of
input from typical customers expressing preferences and from store managers who understand
product mix and store volumes, where they view the merchandise and run through a series of
exercises designed to bring the group to a consensus estimate. The point is that these are no
wild guesses as to the expected demand—rather, it involves a well-thought-out and structured
decision-making approach.
Forecasting
Chapter 18
These techniques are most useful when the product is new or there is little experience
with selling into a new region. Here such information as knowledge of similar products, the
habits of customers in the area, and how the product will be advertised and introduced may be
important to estimate demand successfully. In some cases, it may even be useful to consider
industry data and the experience of competing firms in making estimates of expected demand.
The following are samples of qualitative forecasting techniques.
M ar ke t Re s e a r ch
Firms often hire outside companies that specialize in market research to conduct this type
of forecasting. You may have been involved in market surveys through a marketing class.
Certainly, you have not escaped telephone calls asking you about product preferences, your
income, habits, and so on.
Market research is used mostly for product research in the sense of looking for new product
ideas, likes and dislikes about existing products, which competitive products within a particular class are preferred, and so on. Again, the data collection methods are primarily surveys
and interviews.
Pan e l Cons e ns us
In a panel consensus, the idea that two heads are better than one is extrapolated to the idea
that a panel of people from a variety of positions can develop a more reliable forecast than a
narrower group. Panel forecasts are developed through open meetings with a free exchange
of ideas from all levels of management and individuals. The difficulty with this open style is
that lower-level employees are intimidated by higher levels of management. For example, a
salesperson in a particular product line may have a good estimate of future product demand
but may not speak up to refute a much different estimate given by the vice president of marketing. The Delphi technique (which we discuss shortly) was developed to try to correct this
impairment to free exchange.
When decisions in forecasting are at a broader, higher level (as when introducing a new
product line or concerning strategic product decisions such as new marketing areas), the term
executive judgment is generally used. The term is self-explanatory: a higher level of management is involved.
H i s t or ica l Ana logy
In trying to forecast demand for a new product, an ideal situation would be one where an
existing product or generic product could be used as a model. There are many ways to classify
such analogies—for example, complementary products, substitutable or competitive products, and products as a function of income. Again, you have surely gotten a deluge of mail
advertising products in a category similar to a product purchased via catalog, the Internet, or
mail order. If you buy a DVD through the mail, you will receive more mail about new DVDs
and DVD players. A causal relationship would be that demand for compact discs is caused by
demand for DVD players. An analogy would be forecasting the demand for digital videodisc
players by analyzing the historical demand for VCRs. The products are in the same general
category of electronics and may be bought by consumers at similar rates. A simpler example
would be toasters and coffeepots. A firm that already produces toasters and wants to produce
coffeepots could use the toaster history as a likely growth model.
D e l p h i M e thod
As we mentioned under panel consensus, a statement or opinion of a higher-level person will
likely be weighted more than that of a lower-level person. The worst case is where lower-level
people feel threatened and do not contribute their true beliefs. To prevent this problem, the
Delphi method conceals the identity of the individuals participating in the study. Everyone
has the same weight. Procedurally, a moderator creates a questionnaire and distributes it to
participants. Their responses are summed and given back to the entire group along with a new
set of questions.
469
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Supply and Demand Planning and Control
Section 4
The step-by-step procedure for the Delphi method is:
1.
2.
3.
4.
5.
Choose the experts to participate. There should be a variety of knowledgeable people
in different areas.
Through a questionnaire (or e-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants.
Summarize the results, and redistribute them to the participants along with appropriate new questions.
Summarize again, refining forecasts and conditions, and again develop new
questions.
Repeat step 4 if necessary. Distribute the final results to all participants.
The Delphi technique can usually achieve satisfactory results in three rounds. The time
required is a function of the number of participants, how much work is involved for them to
develop their forecasts, and their speed in responding.
WEB-BASED FORECAST ING: COLLABORATIVE PLANNING,
FOR ECASTING, AND REPLENISHMENT (CPFR)
LO 18–4
Apply collaborative
techniques to forecast
demand.
Collaborative planning,
forecasting, and
replenishment (CPFR)
An Internet tool to
coordinate forecasting,
production, and purchasing
in a firm’s supply chain.
Collaborative planning, forecasting, and replenishment (CPFR) is a Web-based tool used
to coordinate demand forecasting, production and purchase planning, and inventory replenishment between supply chain trading partners. CPFR is being used as a means of integrating
all members of an n-tier supply chain, including manufacturers, distributors, and retailers. As
depicted in Exhibit 18.17, the ideal point of collaboration utilizing CPFR is the retail-level
demand forecast, which is successively used to synchronize forecasts, production, and replenishment plans upstream through the supply chain.
Although the methodology is applicable to any industry, CPFR applications to date have
largely focused on the food, apparel, and general merchandise industries. The potential benefits of sharing information for enhanced planning visibility in any supply chain are enormous.
Various estimates for cost savings attributable to improved supply chain coordination have
been proposed, including $30 billion annually in the food industry alone.
CPFR’s objective is to exchange selected internal information on a shared Web server in
order to provide for reliable, longer-term future views of demand in the supply chain. CPFR
uses a cyclic and iterative approach to derive consensus supply chain forecasts. It consists of
the following five steps:
Step 1. Creation of a front-end partnership agreement. This agreement specifies (1)
objectives (e.g., inventory reductions, lost sales elimination, lower product obsolescence) to
be gained through collaboration, (2) resource requirements (e.g., hardware, software, performance metrics) necessary for the collaboration, and (3) expectations of confidentiality
exhibit 18.17
“Tier n”
Vendor
Tier 3
Vendor
n-Tier Supply Chain with Retail Activities
Tier 2
Vendor
Tier 1
Vendor
Production Planning
and Purchase Information
Fabrication and
Final Assembly
Distribution
Center
Retailer
Replenishment Forecast
Information Information
Note: Solid arrows represent material flows; dashed arrows represent information flows.
Forecasting
Chapter 18
471
concerning the prerequisite trust necessary to share sensitive company information, which
represents a major implementation obstacle.
Step 2. Joint business planning. Typically, partners create partnership strategies, design
a joint calendar identifying the sequence and frequency of planning activities to follow
that affect product flows, and specify exception criteria for handling planning variances
between the trading partners’ demand forecasts.
Step 3. Development of demand forecasts. Forecast development may follow preexisting company procedures. Retailers should play a critical role because shared point-of-sale
(POS) data permit the development of more accurate and timely expectations (compared
with extrapolated warehouse withdrawals or aggregate store orders) for both retailers and
vendors. Given the frequency of forecast generation and the potential for vast numbers of
items requiring forecast preparation, a simple forecast procedure such as a moving average
is commonly used within CPFR. Simple techniques are easily used in conjunction with
expert knowledge of promotional or pricing events to modify forecast values accordingly.
Step 4. Sharing forecasts. Retailer (order forecasts) and vendor (sales forecasts) then
electronically post their latest forecasts for a list of products on a shared server. The server
examines pairs of corresponding forecasts and issues an exception notice for any forecast pair where the difference exceeds a preestablished safety margin (e.g., 5 percent). If
the safety margin is exceeded, planners from both firms may collaborate electronically to
derive a consensus forecast.
Step 5. Inventory replenishment. Once the corresponding forecasts are in agreement,
the order forecast becomes an actual order, which commences the replenishment process.
Each of these steps is then repeated iteratively in a continuous cycle, at varying times, by
individual products, and the calendar of events is established between trading partners. For
example, partners may review the front-end partnership agreement annually, evaluate the
joint business plans quarterly, develop forecasts weekly to monthly, and replenish daily.
The early exchange of information between trading partners provides for reliable, longerterm future views of demand in the supply chain. The forward visibility based upon information sharing leads to a variety of benefits within supply chain partnerships.
As with most new corporate initiatives, there is skepticism and resistance to change. One of
the largest hurdles hindering collaboration is the lack of trust over complete information sharing between supply chain partners. The conflicting objective between the profit-­maximizing
vendor and the cost-minimizing customer gives rise to adversarial supply chain relationships.
Sharing sensitive operating data may enable one trading partner to take advantage of the
other. Similarly, there is the potential loss of control as a barrier to implementation. Some
companies are rightfully concerned about the idea of placing strategic data such as financial
reports, manufacturing schedules, and inventory values online. Companies open themselves
up to security breaches. However, front-end partnership agreements, nondisclosure agreements, and limited information access may help overcome these fears.
Concept Connections
LO 18–1 Understand how forecasting is essential to supply chain planning.
Summary
Forecasts are essential to every business organization. It
is important to consider the purpose of the forecast before
selecting the technique.
∙ Tactical forecasts would cover only a short period of
time, at most a few weeks in the future, and would
typically be for individual items.
∙ Strategic forecasts are typically longer term and usually
involve forecasting demand for a group of products.
Forecasts are used in many different problems studied in this book.
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Supply and Demand Planning and Control
Key Terms
Strategic forecasts Medium and long-term forecasts
that are used for decisions related to strategy and aggregate demand.
Tactical forecasts Short-term forecasts used for making
day-to-day decisions related to meeting demand.
LO 18–2 Evaluate demand using quantitative forecasting models.
Summary
In this chapter, the focus is on time series analysis techniques. With a time series analysis, past demand data are
used to predict future demand.
∙ Demand can be broken down or “decomposed” into
basic elements, such as trend, seasonality, and random
variation (there are other elements, but these are the
ones considered in this chapter).
∙ Four different time series models are evaluated: simple moving average, weighted moving average, exponential smoothing, and linear regression.
∙ Trend and seasonal components are analyzed for these
problems.
∙ Causal relationship forecasting is different from time
series (but commonly used) because it uses data other
than past demand in making the forecast.
∙ The quality of a forecast is measured based on its
error. Various measures exist, including the average
error, percentage of error, and bias. Bias occurs when
a forecast is consistently higher or lower than actual
demand.
Key Terms
Time series analysis A forecast in which past demand
data is used to predict future demand.
Moving average A forecast based on average past demand.
Weighted moving average A forecast made with past
data where more recent data is given more significance
than older data.
Exponential smoothing A time series forecasting technique using weights that decrease exponentially (1 – α)
for each past period.
Smoothing constant alpha (α) The parameter in the exponential smoothing equation that controls the speed of reaction to differences between forecasts and actual demand.
Smoothing constant delta (δ) An additional parameter
used in an exponential smoothing equation that includes
an adjustment for trend.
Linear regression forecasting A forecasting technique
that fits a straight line to past demand data.
Decomposition The process of identifying and separat-
ing time series data into fundamental components such
as trend and seasonality.
Forecast error The difference between actual demand
and what was forecast.
Mean absolute deviation (MAD) The average of the
absolute value of the actual forecast error.
Mean absolute percent error (MAPE) The average error
measured as a percentage of average demand.
Tracking signal A measure of whether the forecast is
keeping pace with any genuine upward or downward
changes in demand. This is used to detect forecast bias.
Causal relationship forecasting Forecasting using
independent variables other than time to predict future
demand.
Key Formulas
​​[18.1]​​
​A​ ​+ ​At−2
​ ​+ ​At−3
​ ​+ . . . +​At−n
​ ​
​​F​​= __________________
​​
​ t−1
t
n
​​[18.2]​​
​ ​+ ​w2​​​At−2
​ ​+ . . . +​wn​​​At−n
​ ​
​​​​Ft​​= ​w1​​​At−1
​​[18.3]​​
​  ​​ + α(​At−1
​  ​​ − ​F​ t−1​​ )​​
​​​Ft​  ​​ = ​Ft−1
​​[18.4]​​
Ft = FITt–1 + α(At–1 – FITt–1)
​​[18.5]​​
Tt = Tt–1 + δ(Ft – FITt–1)
​​[18.6]​​
FITt = Ft + Tt
​​[18.7]​​
​​Y = a + bt​​
​​[18.8]​​
∑ t ​y​ − n​t¯​​·y ​
​  ¯​  ​​
b = __________
​​
​​
2
2
¯
∑ ​t​ ​ − n t​ ​ ​
​​[18.9]​​
​ ¯ − b​ t ​¯​​​​
​​a = y ​
Forecasting
√
__________
​​
n
​​​​LO 18–3
|
|
​∑​  ​​​​ ​​ ​At​  ​​ − ​F​ t​​​ ​​​
​​
​​
t=1
MAD = ​ ________
n ​
​​[18.11]​​
​​[18.12]​​
⎡ ​​At​  ​​ – ​F​ t​​ ​⎤
n ⎢_____
⎥​​​​
​​MAPE ​ = ___
​  100
n ​ ​∑ t=1​​​​⎣​  ​A​   ​
​​ ⎦
t
​​[18.13]​​
RSFE ​​​
​​TS = ​ _____
MAD
|
n
​∑​  ​​ ​(y​ i​  ​​ − ​Y​ i​​ )​​  2​
​​​​
__________
​Syt​  ​​ = ​ ​  i=1
​ ​
n−2
​​[18.10]​​
473
Chapter 18
|
Apply qualitative techniques to forecast demand.
Summary
∙ Qualitative techniques depend more on judgment or
the opinions of experts and can be useful when past
demand data are not available.
∙ These techniques typically involve a structured process so that experience can be acquired and accuracy
assessed.
LO 18–4 Apply collaborative techniques to forecast demand.
Summary
∙ Collaboration between supply chain partners, such as
the manufacturer and the retailer selling a product, can
be useful.
∙ Typically, Web-based technology is used to derive
a forecast that is a consensus of all the participants.
There are often great benefits to all participants due
to the sharing of information and future planning visibility offered through the system.
Key Terms
Collaborative Planning, Forecasting, and Replenishment (CPFR) An Internet tool to coordinate forecasting,
production, and purchasing in a firm’s supply chain.
Solved Problems
SOLVED PROBLEM 1
Sunrise Baking Company markets doughnuts through a chain of food stores. It has been experiencing overproduction and underproduction because of forecasting errors. The following
data are its demand in dozens of doughnuts for the past four weeks. Doughnuts are made
for the following day; for example, Sunday’s doughnut production is for Monday’s sales,
­Monday’s production is for Tuesday’s sales, and so forth. The bakery is closed Saturday, so
Friday’s production must satisfy demand for both Saturday and Sunday.
4 Weeks Ago
3 Weeks Ago
2 Weeks Ago
Last Week
Monday
2,200
2,400
2,300
2,400
Tuesday
2,000
2,100
2,200
2,200
Wednesday
2,300
2,400
2,300
2,500
Thursday
1,800
1,900
1,800
2,000
Friday
1,900
1,800
2,100
2,000
2,700
3,000
2,900
Saturday
Sunday
(closed on Saturday)
2,800
LO 18–2
474
Supply and Demand Planning and Control
Section 4
Make a forecast for this week based on the following:
a. Daily, using a simple four-week moving average.
b. Daily, using a weighted moving average with weights of 0.40, 0.30, 0.20, and 0.10
(most recent to oldest week).
c. Sunrise is also planning its purchases of ingredients for bread production. If bread
demand had been forecast for last week at 22,000 loaves and only 21,000 loaves were
actually demanded, what would Sunrise’s forecast be for this week using exponential
smoothing with α = 0.10?
d. Suppose, with the forecast made in c, this week’s demand actually turns out to be
22,500. What would the new forecast be for the next week?
Solution
a. Simple moving average, four-week.
2,400 + 2,300 + 2,400 + 2,200 _____
9,300
Monday ____________________
​
​ = ​
​= 2,325 doz.
4
4
8,500
Tuesday
= ​_____​= 2,125 doz.
4
9,500
Wednesday
= ​_____​= 2,375 doz.
​
​ ​​ ​
​
​ ​ 4
​​
7,500
Thursday
= _____
​
​= 1,875 doz.
4
7,800
_____
Friday
=​
​= 1,950 doz.
4
11,400
Saturday and Sunday
= _____
​
​= 2,850 doz.
4
b. Weighted average with weights of .40, .30, .20, and .10.
(.10)
(.20)
(.30)
(.40)
Monday
220
+
480
+
690
+
Tuesday
200
+
420
+
660
Wednesday
230
+
480
+
690
Thursday
180
+
380
+
Friday
190
+
360
Saturday and
Sunday
280
+
540
960
=
2,350
+
880
=
2,160
+
1,000
=
2,400
540
+
800
=
1,900
+
630
+
800
=
1,980
+
900
+
1,160
=
2,880
c. Exponentially smoothed forecast for bread demand
​ ​)
​ t​​ = ​Ft−1
F
​ ​+ α(​At−1
​ ​− ​Ft−1
​ − 22,000 )​
​ ​
=​ 22,000 + 0.10(21,000
​ = 22,000 − 100 = 21,900 loaves
d. Exponentially smoothed forecast
​ t+1
F
​ ​ = 21,900 + .10(22,500 – 21,900 )
​ ​
​ ​
​ ​
​ = 21,900 + .10(600 ) = 21,960 loaves
SOLVED PROBLEM 2
Given the following information, make a forecast for May using exponential smoothing with
trend and linear regression.
Month
Demand
January
February
March
April
700
760
780
790
Forecasting
Chapter 18
For exponential smoothing with trend, assume that the previous forecast (for April) including
trend (FIT) was 800 units, and the previous trend component (T) was 50 units. Also, alpha
(α) = .3 and delta(δ) = .1.
For linear regression, use the January-through-April demand data to fit the regression
line. Use the Excel regression functions SLOPE and INTERCEPT to calculate these values.
Solution
Exponential smoothing with trend
Use the following three steps to update the forecast for each period:
1 Forecast without Trend Ft = FITt−1 + α(At−1− FITt−1)
2 Update Trend estimate Tt =Tt−1 + δ(Ft − FITt−1)
3 New Forecast including Trend FITt =Ft +Tt
​ iven
G
FIT​April​ = 800
​
​ ​ ​
​
and ​TApril
​ ​
= 50
Then
​
​FMay
​ ​ = 800 + .3(790 − 800 ) = 797
​T
​ ​ =​ 50 + .1(797 − 800 ) = 49.7​​
May
​FIT​May​ = 797 + 49.7 = 846.7
Linear regression
1 Set up the problem and calculate the slope and intercept as shown here.
2 Forecast using linear regression
Ft = a + bt
where a is the “Slope” and b is the “Intercept,” and t for May is 5 (the index for month 5).
T
​ hen
​ ​F​May​= 685 + 29​​(​5​)​= 830​
SOLVED PROBLEM 3
The following are quarterly data for the past two years. From these data, prepare a forecast for
the upcoming year using decomposition.
Period
Actual
Period
1
300
5
Actual
416
2
540
6
760
3
885
7
1,191
4
580
8
760
475
476
Supply and Demand Planning and Control
Section 4
Solution
(Note that the values you obtain may be slightly different due to rounding. The values given
here were obtained using an Excel spreadsheet.)
(1)
Period
x
(2)
Actual
y
(3)
Period
average
(4)
Seasonal
factor
(5)
Deseasonalized
demand yd
1
2
3
4
5
6
7
8
300
540
885
580
416
760
1,191
760
358
650
1,038
670
0.527
0.957
1.529
0.987
0.527
0.957
1.529
0.987
568.99
564.09
578.92
587.79
789.01
793.91
779.08
770.21
Total
5,432
2,716
8.0
679
679
Average
1
Column 3 is seasonal average. For example, the first-quarter average is
300 + 416
_______
​
​= 358​
2
Column 4 is the quarter average (column 3) divided by the overall average (679). Column 5 is
the actual data divided by the seasonal index. To determine t2 and ty, we can construct a table
as follows:
Period t
Deseasonalized
Demand (yd)
1
568.99
1
569.0
2
564.09
4
1,128.2
3
578.92
9
1,736.7
4
587.79
16
2,351.2
5
789.01
25
3,945.0
6
793.91
36
4,763.4
7
779.08
49
5,453.6
8
Sums
Average
36
4.5
t2
770.21
5,432
tyd
64
6,161.7
204
26,108.8
679
Now we calculate regression results for deseasonalized data.
​(​26108.8​)​− ​(​8​)​(​4.5​)​(​679​)​
b = ​_________________
​= 39.64
​(​204​)​− ​(​8​)​(​4.5​)​2​
​​
​  ​
​
​​​
a = y ​
​​  ¯d​  ​​ − b​ t ​¯
a = 679 − 39.64​​(​4.5​)​= 500.6
Therefore, the deseasonalized regression results are
​Y = 500.6 + 39.64t​
Forecasting
Period
Trend Forecast
9
857.4
×
Seasonal Factor
0.527
=
452.0
10
897.0
×
0.957
=
858.7
11
936.7
×
1.529
=
1,431.9
12
976.3
×
0.987
=
963.4
Chapter 18
Final Forecast
SOLVED PROBLEM 4
A specific forecasting model was used to forecast demand for a product. The forecasts and the
corresponding demand that subsequently occurred are shown as follows. Use the MAD, tracking signal technique, and MAPE to evaluate the accuracy of the forecasting model.
Actual
Forecast
October
700
660
November
760
840
December
780
750
January
790
835
February
850
910
March
950
890
Solution
Evaluate the forecasting model using the MAD, the tracking signal, and MAPE.
Actual
Demand
Forecast
Demand
Actual
Deviation
Cumulative
Deviation (RSFE)
October
700
660
40
40
1.00
40 (5.71%)
November
760
840
−80
−40
0.67
80 (10.53%)
December
780
750
30
−10
0.20
30 (3.85%)
January
790
835
−45
−55
1.13
45 (5.70%)
February
850
910
−60
−115
2.25
60 (7.06%)
March
950
890
60
−55
1.05
60 (6.32%)
Average demand = 805
Tracking
Signal
Absolute Deviation
(% Deviation)
Total dev. = 315
MAD = ___
​315 ​= 52.5
6
Tracking
signal​​ =​​ ____
​− 55 ​= − 1.05​
​
​
52.5
​
5 . 71 + 10 . 53 + 3 . 85 + 5 . 70 + 7 . 06 + 6 . 32
MAPE = ____________________________
​
​= 6.53%
6
0
– 1.05
There is not enough evidence to reject the forecasting model, so we accept its recommendations.
477
478
Supply and Demand Planning and Control
Section 4
Discussion Questions
LO 18–1
LO 18–2
LO 18–3
LO 18–4
1. Why is forecasting necessary in OSCM?
2. It is a common saying that the only thing certain about a forecast is that it will be wrong.
What is meant by this?
3. From the choice of the simple moving average, weighted moving average, exponential
smoothing, and linear regression analysis, which forecasting technique would you consider the most accurate? Why?
4. All forecasting methods using exponential smoothing, adaptive smoothing, and exponential smoothing including trend require starting values to get the equations going. How
would you select the starting value for, say, Ft−1?
5. How is a seasonal index computed from a regression line analysis?
6. Discuss the basic differences between the mean absolute deviation and mean absolute
percent error.
7. What implications do forecast errors have for the search for ultrasophisticated statistical
forecasting models?
8. Causal relationships are potentially useful for which component of a time series?
9. Let’s say you work for a company that makes prepared breakfast cereals like corn flakes.
Your company is planning to introduce a new hot breakfast product made from whole
grains that would require some minimal preparation by the consumer. This would be
a completely new product for the company. How would you propose forecasting initial
demand for this product?
10. How has the development of the Internet affected the way companies forecast in support
of their supply chain planning process?
11. What sorts of risks do you see in reliance on the Internet in the use of collaborative planning, forecasting, and replenishment (CPFR)?
Objective Questions
LO 18–1
LO 18–2
1. What is the term for forecasts used for making day-to-day decisions about meeting demand?
2. What category of forecasting techniques uses managerial judgment in lieu of numerical data?
3. Given the following history, use a three-quarter moving average to forecast the demand
for the third quarter of this year. Note, the 1st quarter is Jan, Feb, and Mar; 2nd quarter
Apr, May, Jun; 3rd quarter Jul, Aug, Sep; and 4th quarter Oct, Nov, Dec.
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Last year
100
125
135
175
185
200
150
140
130
200
225
250
This year
125
135
135
190
200
190
4. Here are the data for the past 21 months for actual sales of a particular product:
Last Year
This Year
Last Year
This Year
January
300
275
February
400
375
July
400
350
August
300
March
425
275
350
September
375
April
350
450
425
October
500
May
400
400
November
550
June
460
350
December
500
Develop a forecast for the fourth quarter using a three-quarter, weighted moving average.
Weight the most recent quarter 0.5, the second most recent 0.25, and the third 0.25. Do the
problem using quarters, as opposed to forecasting separate months. (Answer in Appendix D)
Forecasting
Chapter 18
5. The following table contains the number of complaints received in a department store for
the first six months of operation.
Month
Complaints
Month
Complaints
January
36
April
90
February
45
May
108
March
81
June
144
I f a three-month moving average is used to smooth this series, what would have been the
forecast for May?
6. The following tabulations are actual sales of units for six months and a starting forecast
in January. (Answers in Appendix D)
a. Calculate forecasts for the remaining five months using simple exponential smoothing
with α = 0.2.
b. Calculate MAD for the forecasts.
Actual
Forecast
January
100
80
February
94
March
106
April
80
May
68
June
94
7. The following table contains the demand from the last 10 months.
Month
Actual
Demand
Month
Actual
Demand
1
31
6
36
2
34
7
38
3
33
8
40
4
35
9
40
5
37
10
41
a. Calculate the single exponential smoothing forecast for these data using an α of 0.30
and an initial forecast (F1) of 31.
b. Calculate the exponential smoothing with trend forecast for these data using an α
of 0.30, a δ of 0.30, an initial trend forecast (T1) of 1, and an initial exponentially
smoothed forecast (F1) of 30.
c. Calculate the mean absolute deviation (MAD) for each forecast. Which is best?
8. Actual demand for a product for the past three months was
Three months ago
400 units
Two months ago
350 units
Last month
325 units
a. Using a simple three-month moving average, make a forecast for this month.
b. If 300 units were actually demanded this month, what would your forecast be for next
month?
c. Using simple exponential smoothing, what would your forecast be for this month if the
exponentially smoothed forecast for three months ago was 450 units and the smoothing constant was 0.20?
9. Assume an initial starting Ft of 300 units, a trend (Tt) of eight units, an alpha of 0.30, and a
delta of 0.40. If actual demand turned out to be 288, calculate the forecast for the next period.
479
480
Section 4
Supply and Demand Planning and Control
10. The number of cases of merlot wine sold by the Connor Owen winery in an eight-year
period is as follows.
Year
Cases of
Merlot Wine
Year
Cases of
Merlot Wine
1
270
5
358
2
356
6
500
3
398
7
410
4
456
8
376
Using an exponential smoothing model with an alpha value of 0.20, estimate the
smoothed value calculated as of the end of year 8. Use the average demand for years 1
through 3 as your initial forecast, and then smooth the forecast forward to year 8.
11. Not all the items in your office supply store are evenly distributed as far as demand is
concerned, so you decide to forecast demand to help plan your stock. Past data for legalsized yellow tablets for the month of August are
Week 1
300
Week 2
400
Week 3
600
Week 4
700
a. Using a three-week moving average, what would you forecast the next week to be?
b. Using exponential smoothing with α = 0.20, if the exponential forecast for week 3 was
estimated as the average of the first two weeks [(300 + 400)/2 = 350], what would you
forecast week 5 to be?
12. Assume that your stock of sales merchandise is maintained based on the forecast demand.
If the distributor’s sales personnel call on the first day of each month, compute your forecast sales by each of the three methods requested here.
Actual
June
140
July
180
August
170
a. Using a simple three-month moving average, what is the forecast for September?
b. Using a weighted moving average, what is the forecast for September with weights of
0.20, 0.30, and 0.50 for June, July, and August, respectively?
c. Using single exponential smoothing and assuming that the forecast for June had been
130, forecast sales for September with a smoothing constant alpha of 0.30.
13. Historical demand for a product is as follows.
Demand
Demand
April
60
July
60
May
55
August
80
June
75
September
75
a. Using a simple four-month moving average, calculate a forecast for October.
b. Using single exponential smoothing with α = 0.2 and a September forecast = 65, calculate a forecast for October.
c. Using simple linear regression, calculate the trend line for the historical data. Let’s say
the X axis is April = 1, May = 2, and so on, while the Y axis is demand.
d. Calculate a forecast for October using your regression formula.
Forecasting
Chapter 18
14. Demand for stereo headphones and MP3 players for joggers has caused Nina Industries
to grow almost 50 percent over the past year. The number of joggers continues to expand,
so Nina expects demand for headsets to also expand, because, as yet, no safety laws have
been passed to prevent joggers from wearing them. Demand for the players for last year
was as follows.
Month
Demand
(units)
January
4,200
July
5,300
February
4,300
August
4,900
March
4,000
September
5,400
April
4,400
October
5,700
May
5,000
November
6,300
June
4,700
December
6,000
Demand
(units)
Month
a. Using linear regression analysis, what would you estimate demand to be for each month
next year? Using a spreadsheet, follow the general format in Exhibits 18.7 and 18.8.
Compare your results to those obtained by using the forecast spreadsheet function.
b. To be reasonably confident of meeting demand, Nina decides to use three standard
errors of estimate for safety. How many additional units should be held to meet this
level of confidence?
15. Historical demand for a product is
Demand
January
12
February
11
March
15
April
12
May
16
June
15
a. Using a weighted moving average with weights of 0.60, 0.30, and 0.10, find the July
forecast.
b. Using a simple three-month moving average, find the July forecast.
c. Using single exponential smoothing with α = 0.2 and a June forecast = 13, find the
July forecast. Make whatever assumptions you wish.
d. Using simple linear regression analysis, calculate the regression equation for the preceding demand data.
e. Using the regression equation in d, calculate the forecast for July.
16. The tracking signals computed using past demand history for three different products are
as follows. Each product used the same forecasting technique.
TS 1
TS 2
TS 3
1
−2.70
1.54
0.10
2
−2.32
−0.64
0.43
3
−1.70
2.05
1.08
4
−1.10
2.58
1.74
5
−0.87
−0.95
1.94
6
−0.05
−1.23
2.24
7
0.10
0.75
2.96
8
0.40
−1.59
3.02
9
1.50
0.47
3.54
10
2.20
2.74
3.75
Discuss the tracking signals for each and what the implications are.
481
482
Supply and Demand Planning and Control
Section 4
17. Here are the actual tabulated demands for an item for a nine-month period (January
through September). Your supervisor wants to test two forecasting methods to see which
method was better over this period.
Month
Actual
January
110
Month
June
Actual
180
February
130
July
140
March
150
August
130
April
170
September
140
May
160
a. Forecast April through September using a three-month moving average.
b. Use simple exponential smoothing with an alpha of 0.3 to estimate April through
­September, using the average of January through March as the initial forecast for April.
c. Use MAD to decide which method produced the better forecast over the six-month
period.
18. A particular forecasting model was used to forecast a six-month period. Here are the
forecasts and actual demands that resulted:
Forecast
Actual
April
250
200
May
325
250
June
400
325
July
350
300
August
375
325
September
450
400
Find the tracking signal and state whether you think the model being used is giving
acceptable answers.
19. Harlen Industries has a simple forecasting model: Take the actual demand for the same
month last year and divide that by the number of fractional weeks in that month. This gives
the average weekly demand for that month. This weekly average is used as the weekly
forecast for the same month this year. This technique was used to forecast eight weeks for
this year, which are shown as follows, along with the actual demand that occurred.
The following eight weeks show the forecast (based on last year) and the demand that
actually occurred:
Week
Forecast
Demand
Actual
Demand
1
140
137
2
140
133
3
140
150
4
140
160
5
140
180
6
150
170
7
150
185
8
150
205
a. Compute the MAD of forecast errors.
b. Using the RSFE, compute the tracking signal.
c. Based on your answers to parts (a) and (b), comment on Harlen’s method of forecasting.
Forecasting
Chapter 18
20. In this problem, you are to test the validity of your forecasting model. Here are the forecasts for a model you have been using and the actual demands that occurred:
Week
Forecast
Actual
1
800
900
2
850
1,000
3
950
1,050
4
950
900
5
1,000
900
6
975
1,100
se the method stated in the text to compute MAD and the tracking signal. Then, decide
U
whether the forecasting model you have been using is giving reasonable results.
21. The following table shows predicted product demand using your particular forecasting
method along with the actual demand that occurred. (Answers in Appendix D)
Forecast
Actual
1,500
1,550
1,400
1,500
1,700
1,600
1,750
1,650
1,800
1,700
a. Compute the tracking signal using the mean absolute deviation and running sum of
forecast errors.
b. Discuss whether your forecasting method is giving good predictions.
22. Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you
would utilize.
Month
Actual
Demand
1
62
7
76
2
65
8
78
3
67
9
78
4
68
10
80
5
71
11
84
6
73
12
85
Month
Actual
Demand
a. Calculate the simple three-month moving average forecast for periods 4 to 12.
b. Calculate the weighted three-month moving average using weights of 0.50, 0.30, and
0.20 for periods 4 to 12.
c. Calculate the single exponential smoothing forecast for periods 2 to 12 using an initial
forecast (F1) of 61 and an α of 0.30.
d. Calculate the exponential smoothing with trend component forecast for periods 2 to 12
using an initial trend forecast (T1) of 1.8, an initial exponential smoothing forecast (F1)
of 60, an α of 0.30, and a δ of 0.30.
e. Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in periods 4 to 12. Which forecasting method do you prefer?
483
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Supply and Demand Planning and Control
23. After using your forecasting model for six months, you decide to test it using MAD and a
tracking signal. Here are the forecast and actual demands for the six-month period:
Period
Forecast
Actual
May
450
500
June
500
550
July
550
400
August
600
500
September
650
675
October
700
600
a. Find the tracking signal.
b. Decide whether your forecasting routine is acceptable.
24. Zeus Computer Chips, Inc. used to have major contracts to produce the Centrino-type
chips. The market has been declining during the past three years because of the quad-core
chips, which it cannot produce, so Zeus has the unpleasant task of forecasting next year.
The task is unpleasant because the firm has not been able to find replacement chips for its
product lines. Here is the demand over the past 12 quarters:
Two
Years Ago
I
II
III
IV
Last
Year
4,800
3,500
4,300
3,000
I
II
III
IV
This
Year
3,500
2,700
3,500
2,400
I
II
III
IV
3,200
2,100
2,700
1,700
Use the decomposition technique to forecast the demand for the next four quarters.
25. The sales data for two years are as follows. Data are aggregated with two months of sales
in each “period.”
Months
Sales
Months
Sales
January–February
March–April
May–June
July–August
September–October
November–December
109
104
150
170
120
100
January–February
March–April
May–June
July–August
September–October
November–December
115
112
159
182
126
106
a. Plot the data.
b. Fit a simple linear regression model to the sales data.
c. In addition to the regression model, determine multiplicative seasonal index factors. A
full cycle is assumed to be a full year.
d. Using the results from parts (b) and (c), prepare a forecast for the next year.
26. The following table shows the past two years of quarterly sales information. Assume that
there are both trend and seasonal factors and that the seasonal cycle is one year. Use time
series decomposition to forecast quarterly sales for the next year.
Quarter
Last Year
Sales
Quarter
This Year
Sales
I
II
III
IV
215
240
205
190
I
II
III
IV
160
195
150
140
Forecasting
Chapter 18
27. Tucson Machinery, Inc. manufactures numerically controlled machines, which sell for an
average price of $0.5 million each. Sales for these NCMs for the past two years were as
follows.
Quarter
Quantity (Units)
Last Year
I
II
III
IV
12
18
26
16
Quarter
Quantity (Units)
This Year
I
II
III
IV
16
24
28
18
a. Find a line using regression in Excel.
b. Find the trend and seasonal factors.
c. Forecast sales for next year.
28. Use regression analysis on deseasonalized demand to forecast next summer’s demand,
given the following historical demand data.
Year
Season
Actual
Demand
2 years ago
Spring
205
Summer
140
Fall
375
Winter
575
Spring
475
Summer
275
Fall
685
Winter
965
Last year
29. The following are earnings per share for two companies by quarter from the first quarter
three years ago through the second quarter of this year. Forecast earnings per share for
the rest of this year and next year. Use exponential smoothing to forecast the third period
of this year, and the time series decomposition method to forecast the last two quarters of
this year and all four quarters of next year. (It is much easier to solve this problem on a
computer spreadsheet so you can see what is happening.)
Earnings per Share
Quarter
3 years ago
2 years ago
Last year
Company B
I
$1.67
$0.17
II
2.35
0.24
III
1.11
0.26
IV
1.15
0.34
I
1.56
0.25
II
2.04
0.37
III
1.14
0.36
IV
0.38
0.44
0.29
0.33
I
II
−0.18 (loss)
0.40
III
−0.97 (loss)
0.41
IV
This year
Company A
0.20
0.47
I
−1.54 (loss)
0.30
II
0.38
0.47
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Section 4
Supply and Demand Planning and Control
a. For the exponential smoothing method, choose the first quarter of three years ago as
the beginning forecast. Make two forecasts: one with α = 0.10 and one with α = 0.30.
b. Using the MAD method of testing the forecasting model’s performance, plus actual
data from three years ago through the second quarter of this year, how well did the
model perform?
c. Using the decomposition of a time series method of forecasting, forecast earnings per
share for the last two quarters of this year and all four quarters of next year. Is there a
seasonal factor in the earnings?
d. Using your forecasts, comment on each company.
30. Mark Price, the new productions manager for Speakers and Company, needs to find out
which variable most affects the demand for their line of stereo speakers. He is uncertain
whether the unit price of the product or the effects of increased marketing are the main
drivers in sales and wants to use regression analysis to figure out which factor drives
more demand for its particular market. Pertinent information was collected by an extensive marketing project that lasted over the past 12 years (year 1 is data from 12 years ago)
and was reduced to the data that follow.
Year
Sales/Unit
(thousands)
Advertising
($000)
Price/Unit
1
400
280
2
700
215
600
835
3
900
211
1,100
4
1,300
210
1,400
5
1,150
215
1,200
6
1,200
200
1,300
7
900
225
900
8
1,100
207
1,100
9
980
220
700
10
1,234
211
900
11
925
227
700
12
800
245
690
a. Perform a regression analysis based on these data using Excel. Answer the following
questions based on your results.
b. Which variable, price or advertising, has a larger effect on sales and how do you
know?
c. Predict average yearly speaker sales for Speakers and Company based on the regression results if the price was $300 per unit and the amount spent on advertising (in
thousands) was $900.
31. Sales by quarter for last year and the first three quarters of this year were as follows.
Quarter
I
II
III
IV
Last year
$23,000
$27,000
$18,000
$9,000
This year
19,000
24,000
15,000
Using a procedure that you develop that captures the change in demand from last year
to this year and also the seasonality in demand, forecast expected sales for the fourth
quarter of this year.
32. The following are sales revenues for a large utility company for years 1 through 11. Forecast revenue for years 12 through 15. Because we are forecasting four years into the
future, you will need to use linear regression as your forecasting method.
Forecasting
Year
Revenue
(millions)
1
$4,865.9
2
5,067.4
3
5,515.6
4
5,728.8
5
5,497.7
6
5,197.7
7
5,094.4
8
5,108.8
9
5,550.6
10
5,738.9
11
5,860.0
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Chapter 18
33. What forecasting technique makes use of written surveys or telephone interviews?
34. Which qualitative forecasting technique was developed to ensure that the input from
every participant in the process is weighted equally?
35. When forecasting demand for new products, sometimes firms will use demand data from
similar existing products to help forecast demand for the new product. What technique is
this an example of?
36. Often, firms will work with their partners across the supply chain to develop forecasts
and execute production and distribution between the partners. What technique does this
describe?
37. How many steps are there in collaborative planning, forecasting, and replenishment
(CPFR)?
38. What is the first step in CPFR?
LO 18–3
LO 18–4
Analytics Exercise: Forecasting Supply Chain Demand—Starbucks
Corporation (LO 18–2)
As we discussed at the beginning of the chapter, Starbucks has a large, global supply chain that must efficiently
supply over 17,000 stores. Although the stores might
appear to be very similar, they are actually very different.
Depending on the location of the store, its size, and the
profile of the customers served, Starbucks management
configures the store offerings to take maximum advantage of the space available and customer preferences.
Starbucks’ actual distribution system is much more
complex, but for the purpose of our exercise let’s focus
on a single item that is currently distributed through five
distribution centers in the United States. Our item is a
logo-branded coffeemaker that is sold at some of the larger
retail stores. The coffeemaker has been a steady seller over
the years due to its reliability and rugged construction.
Starbucks does not consider this a seasonal product, but
there is some variability in demand. Demand for the product over the past 13 weeks is shown in the following table.
The demand at the distribution centers (DCs) varies
between about 40 units, on average, per week in Atlanta
and 48 units in Dallas. The current quarter’s data are
pretty close to the demand shown in the table.
Management would like you to experiment with
some forecasting models to determine what should be
used in a new system to be implemented. The new system is programmed to use one of two forecasting models:
simple moving average or exponential smoothing.
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
Atlanta
33
45
37
38
55
30
18
58
47
37
23
55
40
40
Boston
26
35
41
40
46
48
55
18
62
44
30
45
50
42
Chicago
44
34
22
55
48
72
62
28
27
95
35
45
47
47
Dallas
27
42
35
40
51
64
70
65
55
43
38
47
42
48
LA
32
43
54
40
46
74
40
35
45
38
48
56
50
46
162
199
189
213
246
288
245
204
236
257
174
248
229
222
Total
Average
488
Supply and Demand Planning and Control
Section 4
Questions
1. Consider using a simple moving average model.
Experiment with models using five weeks’ and three
weeks’ past data. The past data in each region are
given as follows (week −1 is the week before week
1 in the table, −2 is two weeks before week 1, etc.).
Evaluate the forecasts that would have been made
over the 13 weeks using the overall (at the end of the
13 weeks) mean absolute deviation, mean absolute
percent error, and tracking signal as criteria.
Week
−5
−4
−3
−2
−1
Atlanta
45
38
30
58
37
Boston
62
18
48
40
35
Chicago
62
22
72
44
48
Dallas
42
35
40
64
43
LA
43
40
54
46
35
254
153
244
252
198
Total
2. Next, consider using a simple exponential smoothing model. In your analysis, test two alpha values,
0.2 and 0.4. Use the same criteria for evaluating
the model as in part 1. When using an alpha value
of 0.2, assume that the forecast for week 1 is the
past three-week average (the average demand for
periods −3, −2, and −1). For the model using an
alpha of 0.4, assume that the forecast for week 1 is
the past five-week average.
3. Starbucks is considering simplifying the supply
chain for their coffeemaker. Instead of stocking
the coffeemaker in all five distribution centers,
they are considering only supplying it from a
single location. Evaluate this option by analyzing how accurate the forecast would be based on
the demand aggregated across all regions. Use the
model that you think is best from your analysis of
parts 1 and 2. Evaluate your new forecast using
mean absolute deviation, mean absolute percent
error, and the tracking signal.
4. What are the advantages and disadvantages of
aggregating demand from a forecasting view? Are
there other things that should be considered when
going from multiple DCs to a DC?
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. This is a type of forecast used to make long-term
decisions, such as where to locate a warehouse or
how many employees to have in a plant next year.
2. This is the type of demand that is most appropriate
for using forecasting models.
3. This is a term used for actually influencing the sale
of a product or service.
4. These are the six major components of demand.
5. This type of analysis is most appropriate when the
past is a good predictor of the future.
6. This is identifying and separating time series data
into components of demand.
7. If the demand in the current week was 102 units and
we had forecast it to be 125, what would be next
week’s forecast using an exponential smoothing
model with an alpha of 0.3?
8. Assume you are using exponential smoothing with
an adjustment for trend. Demand is increasing at a
very steady rate of about five units per week. Would
you expect your alpha and delta parameters to be
closer to one or zero?
9. Your forecast is, on average, incorrect by about 10
percent. The average demand is 130 units. What is
the MAD?
10. If the tracking signal for your forecast was consistently positive, you could then say this about your
forecasting technique.
11. What would you suggest to improve the forecast
described in question 10?
12. You know that sales are greatly influenced by the
amount your firm advertises in the local paper. What
forecasting technique would you suggest trying?
13. What forecasting tool is most appropriate when closely
working with customers dependent on your products?
Answers to Practice Exam 1. Strategic forecast 2. Independent demand 3. Demand management 4. Average demand for the period, trend,
seasonal elements, cyclical elements, random variation, and autocorrelation 5. Time series analysis 6. Decomposition 7. 118 units 8. Zero 9. 13
10. Biased, consistently too low 11. Add a trend component 12. Causal relationship forecasting (using regression) 13. Collaborative planning,
forecasting, and replenishment (CPFR)
Sales and
Operations
Planning
19
Learning Objectives
LO19–1Understand what sales and operations planning is and how it
coordinates manufacturing, logistics, service, and marketing plans.
LO19–2Construct and evaluate aggregate plans that employ different
strategies for meeting demand.
LO19–3 Explain yield management and why it is an important strategy.
Consider the dilemma of the executive staff at Southwest Manufacturing Company at their monthly planning meeting. Things are tough and it seems that
everyone is complaining.
∙
The president has been reviewing reports from marketing. “We keep running out of product. How can we sell stuff if we don’t have it when the customer wants it? And the response time on customer questions is terrible. It is
often days between when the question comes in and when we get around to
responding. This cannot continue.”
∙
The supply chain executive responds, “Our forecast from marketing was terrible last month. They sold 30 percent more than they had forecast. How do
you expect us to keep this stuff in stock?”
∙
Marketing chimes in with, “We had a great month, what are you complaining
about? We told you mid-month that things were going well.” The plant manager replies, “There is no way that we can react that
quickly. What are you expecting from us? Our schedules are fixed six weeks into the future. You want us
to be efficient, don’t you?”
∙
The president asks, “Should we just bump everything
up 30 percent for next month? I sure don’t want to
run out again.”
∙
Marketing responds, “Only if you are willing to keep running that 2-for-1 deal that we were running last month.
Our customers pass that discount on to their customers
and that keeps sales going. I am not sure that we are
making much money when we discount like that.”
∙
This wakes up the finance guy, “Oh, so now I understand why we have such a big negative revenue variance. We can’t give the stuff away anymore.”
© Lane Oatey/Getty Images RF
489
This struggle between those selling the product, those supplying the product, and
those keeping track of the money goes on month after month. The problem is one of
matching supply with demand at a price that makes the firm profitable. It is a difficult
balancing act and one that plays out at most companies.
Today, many companies are using a business process called sales and operations
planning (S&OP) to help avoid such problems. This chapter defines S&OP and discusses how to make it work.
WHAT I S SALES AND O PERATIONS PLANNING?
LO 19–1
Understand what sales
and operations planning
is and how it coordinates
manufacturing, logistics,
service, and marketing
plans.
Aggregate operations
plan
A plan for labor and
production for the
intermediate term with the
objective to minimize the
cost of resources needed
to meet demand.
Sales and operations
planning
The process that
companies use to keep
demand and supply in
balance by coordinating
manufacturing, distribution,
marketing, and financial
plans.
490
In this chapter, we focus on the aggregate operations plan, which translates annual and
quarterly business plans into broad labor and output plans for the intermediate term (3 to 18
months). The objective of the aggregate operations plan is to minimize the cost of resources
required to meet demand over that period.
Sales and operations planning is a process that helps firms provide better customer service, lower inventory, shorten customer lead times, stabilize production rates, and give top
management a handle on the business. The process is designed to coordinate the key business
activities related to marketing and sales with the operations and supply chain activities that
are required to meet demand over time. Depending on the situation, business activities may
include the timing of newspaper advertisements, volume discounting of discontinued items,
and major direct sales promotions, for example. The process is designed to help a company
get demand and supply in balance and keep them in balance over time. The process requires
teamwork among marketing and sales, distribution and logistics, operations, finance, and
product development.
The sales and operations planning process consists of a series of meetings, finishing with
a high-level meeting where key intermediate-term decisions are made. The end goal is an
agreement between various departments on the best course of action to achieve the optimal
balance between supply and demand. The idea is to put the operational plan in line with the
business plan.
This balance must occur at an aggregate level and also at the detailed individual product level. By aggregate we mean at the level of major groups of products. Over time, we
need to ensure that we have enough total capacity. Because demand is often quite dynamic,
it is important that we monitor our expected needs 3 to 18 months or further into the future.
When planning this far into the future, it is difficult to know exactly how many of a particular
product we will need, but we should be able to know how a larger group of similar products
should sell. The term aggregate refers to this group of products. Given that we have enough
aggregate capacity, our individual product schedulers, working within aggregate capacity
constraints, can handle the daily and weekly launching of individual product orders to meet
short-term demand.
A n Ove r vie w o f Sales an d Op eratio n s Plan n in g Activi ti e s
Exhibit 19.1 positions sales and operations planning relative to other major operations planning activities. The term sales and operations planning was coined by companies to refer to
the process that helps firms keep demand and supply in balance. In operations management,
this process traditionally was called aggregate planning. The new terminology is meant to
capture the importance of cross-functional work. Typically, this activity requires an integrated
effort with cooperation from sales, distribution and logistics, operations, finance, and product
development.
Sales and Operations Planning
exhibit 19.1
Chapter 19
491
Overview of Major Operations and Supply Planning Activities
Process planning
Long
range
Supply network
planning
Strategic capacity
planning
Forecasting and
demand management
Sales and operations
(aggregate) planning
Aggregate
Sales plan operations
plan
Medium
range
Short
range
Manufacturing
Logistics
Services
Master scheduling
Vehicle capacity
planning
Weekly workforce
scheduling
Material requirements
planning
Vehicle loading
Order scheduling
Vehicle dispatching
Daily workforce
scheduling
Warehouse receipt
planning
Within sales and operations planning, marketing develops a sales plan that extends through the next 3 to 18
months. This sales plan typically is stated in units of aggregate product groups and often is tied into sales incentive
programs and other marketing activities. The operations
side develops an operations plan as an output of the process, which is discussed in depth in this chapter. By focusing on aggregate product and sales volumes, the marketing
and operations functions are able to develop plans for the
way demand will be met. This is a particularly difficult task
when there are significant changes in demand over time as
a result of market trends or other factors.
Aggregation on the supply side is done by product families, and on the demand side it is done by groups of customers. Individual product production schedules and matching Product family of similar earphones produced by the same
company.
customer orders can be handled more readily as a result of © Future Publishing/Getty Images
the sales and operations planning process. Typically, sales
and operations planning occurs on a monthly cycle. Sales and operations planning links a
company’s strategic plans and business plan to its detailed operations and supply processes.
Long-range planning
These detailed processes include manufacturing, logistics, and service activities, as shown in
One year or more.
Exhibit 19.1.
In Exhibit 19.1, the time dimension is shown as long, intermediate, and short range. Intermediate-range
Long-range planning generally is done annually, focusing on a horizon greater than one planning
year. Intermediate-range planning usually covers a period from 3 to 18 months, with time Involves a time period of
increments that are weekly, monthly, or sometimes quarterly. Short-range planning covers a usually 3 to 18 months.
period from one day to six months, with daily or weekly time increments.
Long-range planning activities are done in two major areas. The first is the design of the Short-range planning
manufacturing and service processes that produce the products of the firm, and the second is From a day to six months.
492
Section 4
Supply and Demand Planning and Control
the design of the logistics activities that deliver products to the customer. Process planning
deals with determining the specific technologies and procedures required to produce a product or service. Strategic capacity planning deals with determining the long-term capabilities
(such as size and scope) of the production systems. Similarly, from a logistics point of view,
supply network planning determines how the product will be distributed to the customer on
the outbound side, with decisions relating to the location of warehouses and the types of
transportation systems to be used. On the inbound side, supply network planning involves
decisions relating to outsourcing production, the selection of parts and component suppliers,
and related decisions.
Intermediate-term activities include forecasting and demand management, as well as sales
and operations planning. The determination of expected demand is the focus of forecasting
and demand management. From these data, detailed sales and operations plans for meeting
these requirements are made. The sales plans are inputs to sales force activities, which are the
focus of marketing books. The operations plan provides input into the manufacturing, logistics, and service planning activities of the firm. Master scheduling and material requirements
planning are designed to generate detailed schedules that indicate when parts are needed for
manufacturing activities. Coordinated with these plans are the logistics plans needed to move
the parts and finished products through the supply chain.
Short-term details are focused mostly on scheduling production and shipment orders.
These orders need to be coordinated with the actual vehicles that transport material through
the supply chain. On the service side, short-term scheduling of employees is needed to ensure
that adequate customer service is provided and fair worker schedules are maintained.
The A ggre g a te Op eratio n s Plan
Production rate
Number of units completed
per unit of time.
Workforce level
Number of workers
needed in a period.
Inventory on hand
Inventory carried from the
previous period.
The aggregate operations plan is concerned with setting production rates by product group or
other broad categories for the intermediate term (3 to 18 months). Note again from Exhibit 19.1
that the aggregate plan precedes the master schedule. The main purpose of the aggregate plan
is to specify the optimal combination of production rate, workforce level, and inventory on
hand. Production rate refers to the number of units completed per unit of time (such as per
hour or per day). Workforce level is the number of workers needed for production (production = production rate × workforce level). Inventory on hand is unused inventory carried
over from the previous period.
Here is a formal statement of the aggregate planning problem: Given the demand forecast
Ft for each period t in the planning horizon that extends over T periods, determine the production level Pt , inventory level It, and workforce level Wt for periods t = 1, 2, . . . , T that minimize the relevant costs over the planning horizon.
The form of the aggregate plan varies from company to company. In some firms, it is a
formalized report containing planning objectives and the planning premises on which it is
based. In other companies, particularly smaller ones, the owner may make simple calculations
of workforce needs that reflect a general staffing strategy.
The process by which the plan itself is derived also varies. One common approach is to
derive it from the corporate annual plan, as shown in Exhibit 19.1. A typical corporate plan
contains a section on manufacturing that specifies how many units in each major product line
need to be produced over the next 12 months to meet the sales forecast. The planner takes
this information and attempts to determine how best to meet these requirements with available resources. Alternatively, some organizations combine output requirements into equivalent units and use this as the basis for the aggregate plan. For example, a division of General
Motors may be asked to produce a certain number of cars of all types at a particular facility.
The production planner would then take the average labor hours required for all models as a
basis for the overall aggregate plan. Refinements to this plan, specifically model types to be
produced, would be reflected in shorter-term production plans.
Another approach is to develop the aggregate plan by simulating various master production schedules and calculating corresponding capacity requirements to see if adequate labor
and equipment exist at each workcenter. If capacity is inadequate, additional requirements for
Sales and Operations Planning
ex hibit 19.2
493
Chapter 19
Required Inputs to the Production Planning System
Competitors’
behavior
Raw material
availability
Market
demand
External
to firm
External
capacity (such as
subcontractors)
Current
physical
capacity
Planning for
production
Current
workforce
Economic
conditions
Inventory
levels
Activities
required for
production
overtime, subcontracting, extra workers, and so forth are specified for each product line and
combined into a rough-cut plan. This plan is then modified by cut-and-try or mathematical
methods to derive a final and (one hopes) lower-cost plan.
T h e P r o d u c t i o n P l a n n i n g E n v i r o n m e n t Exhibit 19.2 illustrates the internal
and external factors that constitute the production planning environment. In general, the
external environment is outside the production planner’s direct control, but in some firms,
demand for the product can be managed. Through close cooperation between marketing and
operations, promotional activities and price cutting can be used to build demand during slow
periods. Conversely, when demand is strong, promotional activities can be curtailed and
prices raised to maximize the revenues from those products or services that the firm has the
capacity to provide. The current practices in managing demand will be discussed later in the
section titled “Yield Management.”
Complementary products may work for firms facing cyclical demand fluctuations. For
instance, lawnmower manufacturers will have strong demand for spring and summer, but
weak demand during fall and winter. Demands on the production system can be smoothed
out by producing a complementary product with high demand during fall and winter, and low
demand during spring and summer (for instance, snowmobiles, snowblowers, or leafblowers).
With services, cycles are more often measured in hours than months. Restaurants with strong
demand during lunch and dinner will often add a breakfast menu to increase demand during
the morning hours.
But even so, there are limits to how much demand can be controlled. Ultimately, the production planner must live with the sales projections and orders promised by the marketing
function, leaving the internal factors as variables that can be manipulated in deriving a production plan. A new approach to facilitate managing these internal factors is termed accurate
response. This entails refined measurement of historical demand patterns blended with expert
judgment to determine when to begin production of particular items. The key element of the
approach is clearly identifying those products for which demand is relatively predictable from
those for which demand is relatively unpredictable.
The internal factors themselves differ in their controllability. Current physical capacity
(plant and equipment) is usually nearly fixed in the short run; union agreements often constrain what can be done in changing the workforce; physical capacity cannot always be
increased; and top management may limit the amount of money that can be tied up in
Internal to
firm
494
Supply and Demand Planning and Control
Section 4
Water skis and snow
skis are examples
of complementary
products.
© Pixtal/AGE fotostock RF
© Ingram Publishing/SuperStock RF
Production planning
strategies
Plans for meeting demand
that involve trade-offs in
the number of workers
employed, work hours,
inventory, and shortages.
inventories. Still, there is always some flexibility in managing these factors, and production
planners can implement one or a combination of the production planning strategies discussed here.
P r o d u c t i o n P l a n n i n g S t r a t e g i e s There are essentially three production
planning strategies. These strategies involve trade-offs among the workforce size, work hours,
inventory, and backlogs.
1.
2.
Pure strategy
A simple strategy that uses
just one option, such as
hiring and firing workers,
for meeting demand.
Mixed strategy
A more complex strategy
that combines options for
meeting demand.
© Pixtal/AGE fotostock RF
3.
Chase strategy. Match the production rate to the order rate by hiring and laying off
employees as the order rate varies. The success of this strategy depends on having
a pool of easily trained applicants to draw on as order volumes increase. There are
obvious motivational impacts. When order backlogs are low, employees may feel
compelled to slow down out of fear of being laid off as soon as existing orders are
completed.
Stable workforce—variable work hours. Vary the output by varying the number of
hours worked through flexible work schedules or overtime. By varying the number
of work hours, you can match production quantities to orders. This strategy provides
workforce continuity and avoids many of the emotional and tangible costs of hiring
and firing associated with the chase strategy.
Level strategy. Maintain a stable workforce working at a constant output rate. Shortages and surpluses are absorbed by fluctuating inventory levels, order backlogs,
and lost sales. Employees benefit from stable work hours at the costs of potentially
decreased customer service levels and increased inventory costs. Another concern is
the possibility of inventoried products becoming obsolete.
When just one of these variables is used to absorb demand fluctuations, it is termed a pure
strategy; two or more used in combination constitute a mixed strategy. As you might suspect, mixed strategies are more widely applied in industry.
S u b c o n t r a c t i n g In addition to these strategies, managers also may choose to
subcontract some portion of production. This strategy is similar to the chase strategy, but
hiring and laying off are translated into subcontracting and not subcontracting. Some level of
Sales and Operations Planning
Chapter 19
495
OSCM AT WORK
It’s All in the Planning
You’re sitting anxiously in the suddenly assembled general
manager’s staff meeting. Voices are nervously subdued.
The rumor mill is in high gear about another initiative-ofthe-month about to be loosed among the leery survivors of
the last purge. The meeting begins. Amid the tricolor visuals and 3D spreadsheets, the same old message is skeptically received by managers scrambling for politically correct
responses in an endless game of shoot the messenger.
This is a familiar scene in corporations around the
world. But interestingly, firms such as Advanced Optical
Components, a division of Finisar, formerly VCSEL, have
learned how to manage the process of successfully matching supply and demand. Advanced Optical Components has
developed a new semiconductor laser used in computing,
networking, and sensing applications. Forecasting and managing production capacity is a unique challenge for companies with a stream of new and innovative products coming
to market. Using a monthly sales and operations planning
process, Advanced Optical Components has been able to
improve its short- and long-term forecasting accuracy from
60 percent to consistently hitting 95 percent or better. The
specific steps within its plan focus the executive team on
(1) the demand opportunities for current and new products
and (2) the constraints on the organization’s ability to produce product to meet this demand. The plan, developed in
a monthly sales and operations planning executive meeting,
ensures that demand is synchronized with supply, so customers get the product they want, when they want it, while
inventory and costs are kept to a minimum.
Advanced Optical Components managers indicated
that a critical step was getting the general manager to
champion the process. The second step was achieving
a complete understanding of required behavior from the
team, including committing to a balanced and synchronized
demand/supply plan, being accountable for meeting the
performance standards, having open and honest communication, not promising what cannot be delivered, and making
the decisions needed to address the identified opportunities and constraints.
subcontracting can be desirable to accommodate demand fluctuations. However, unless the
relationship with the supplier is particularly strong, a manufacturer can lose some control over
schedule and quality.
R e l e v a n t C o s t s Four costs are relevant to the aggregate production plan. These relate to
the production cost itself, as well as the cost to hold inventory and to have unfilled orders. More
specifically, these are
1.
2.
3.
4.
Basic production costs These are the fixed and variable costs incurred in producing a given product type in a given time period. Included are direct and indirect labor
costs and regular as well as overtime compensation.
Costs associated with changes in the production rate Typical costs in this category are those involved in hiring, training, and laying off personnel. Hiring temporary help is a way of avoiding these costs.
Inventory holding costs A major component is the cost of capital tied up in inventory. Other components are storing, insurance, taxes, spoilage, and obsolescence.
Backordering costs Usually, these are very hard to measure and include costs
of expediting, loss of customer goodwill, and loss of sales revenues resulting from
backordering.
B u d g e t s To receive funding, operations managers are generally required to submit
annual, and sometimes quarterly, budget requests. The aggregate plan is key to the success
of the budgeting process. Recall that the goal of the aggregate plan is to minimize the total
production-related costs over the planning horizon by determining the optimal combination
of workforce levels and inventory levels. Thus, the aggregate plan provides justification for
the requested budget amount. Accurate medium-range planning increases the likelihood of (1)
receiving the requested budget and (2) operating within the limits of the budget.
496
Section 4
Supply and Demand Planning and Control
In the next section, we provide an example of medium-range planning in a manufacturing
setting. This example illustrates the trade-offs associated with different production planning
strategies.
AGGR EGATE PLANNING TECHNIQUES
LO 19–2
Construct and evaluate
aggregate plans that
employ different strategies
for meeting demand.
Companies commonly use simple cut-and-try charting and graphic methods to develop aggregate plans. A cut-and-try approach involves costing out various production planning alternatives and selecting the one that is best. Elaborate spreadsheets are developed to facilitate the
decision process. Sophisticated approaches involving linear programming and simulation are
often incorporated into these spreadsheets. In the following, we demonstrate a spreadsheet
approach to evaluate four strategies for meeting demand for the JC Company. Later, we discuss more sophisticated approaches using linear programming (see Appendix A).
A Cut- a nd - Try E xamp le: T h e JC Co mp an y
A firm with pronounced seasonal variation normally plans production for a full year to capture the extremes in demand during the busiest and slowest months. But we can illustrate the
general principles involved with a shorter horizon. Suppose we wish to set up a production
plan for the JC Company’s Chinese manufacturing plant for the next six months. We are given
the following information.
Demand and Working Days
January
February
March
April
May
June
Totals
1,800
1,500
1,100
900
1,100
1,600
8,000
22
19
21
21
22
20
125
Demand forecast
Number of working days
Costs
Materials
Inventory holding cost
Marginal cost of stock out
Marginal cost of subcontracting
$100.00/unit
$1.50/unit/month
$5.00/unit/month
$20.00/unit ($120 subcontracting cost
less $100 material savings)
Hiring and training cost
$200.00/worker
Layoff cost
$250.00/worker
Labor hours required
5/unit
Straight-time cost (first eight hours each day)
$4.00/hour
Overtime cost (time and a half)
$6.00/hour
Inventory
Beginning inventory
400 units
Safety stock
25% of month demand
In solving this problem, we can exclude the material costs. We could have included
this $100 cost in all our calculations, but if we assume that a $100 cost is common to each
demanded unit, then we need only concern ourselves with the marginal costs. Because the
subcontracting cost is $120, our marginal cost that does not include materials is $20.
Note that many costs are expressed in a different form than typically found in the
accounting records of a firm. Therefore, do not expect to obtain all these costs directly
from such records, but obtain them indirectly from management personnel, who can help
interpret the data.
Inventory at the beginning of the first period is 400 units. Because the demand forecast is
imperfect, the JC Company has determined that a safety stock (buffer inventory) should be
established to reduce the likelihood of stock outs. For this example, assume the safety stock
should be one-quarter of the demand forecast. (Chapter 20 covers this topic in depth.)
Sales and Operations Planning
exhibit 19.3
Chapter 19
497
Aggregate Production Planning Requirements
January February March April
Beginning inventory
Demand forecast
Safety stock (.25 × Demand forecast)
Production requirement (Demand forecast + Safety
stock − Beginning inventory)
Ending inventory (Beginning inventory + Production
requirement − Demand forecast)
May
June
400
1,800
450
450
1,500
375
375
1,100
275
275
900
225
225
275
1,100 1,600
275
400
1,850
1,425
1,000
850
1,150 1,725
450
375
275
225
275
400
Before investigating alternative production plans, it is often useful to convert demand forecasts into production requirements, which take into account the safety stock estimates. In
Exhibit 19.3, note that these requirements implicitly assume that the safety stock is never actually used, so that the ending inventory each month equals the safety stock for that month. For
example, the January safety stock of 450 (25 percent of January demand of 1,800) becomes
the inventory at the end of January. The production requirement for January is demand plus
safety stock minus beginning inventory (1,800 + 450 – 400 = 1,850).
Now we must formulate alternative production plans for the JC Company. Using a spreadsheet, we investigate four different plans with the objective of finding the one with the lowest
total cost.
Plan 1. Produce to exact monthly production requirements using a regular eight-hour
day by varying workforce size.
Plan 2. Produce to meet expected average demand over the next six months by maintaining a constant workforce. This constant number of workers is calculated by finding the
average number of workers required each day over the horizon. Take the total production
requirements and multiply by the time required for each unit. Then divide by the total time
that one person works over the horizon [(8,000 units × 5 hours per unit) ÷ (125 days × 8
hours per day) = 40 workers]. Inventory is allowed to accumulate, with shortages filled
from next month’s production by backordering. Negative beginning inventory balances
indicate that demand is backordered. In some cases, sales may be lost if demand is not met.
The lost sales can be shown with a negative ending inventory balance followed by a zero
beginning inventory balance in the next period. Notice that in this plan we use our safety
stock in January, February, March, and June to meet expected demand.
Plan 3. Produce to meet the minimum expected demand (April) using a constant workforce on regular time. Subcontract to meet additional output requirements. The number of
workers is calculated by locating the minimum monthly production requirement and determining how many workers would be needed for that month [(850 units × 5 hours per unit)
÷ (21 days × 8 hours per day) = 25 workers] and subcontracting any monthly difference
between requirements and production.
Plan 4. Produce to meet expected demand for all but the first two months using a constant workforce on regular time. Use overtime to meet additional output requirements. The
number of workers is more difficult to compute for this plan, but the goal is to finish June
with an ending inventory as close as possible to the June safety stock. By trial and error it
can be shown that a constant workforce of 38 workers is the closest approximation.
The next step is to calculate the cost of each plan. This requires the series of simple calculations shown in Exhibit 19.4. Note that the headings in each row are different for each plan
because each is a different problem requiring its own data and calculations.
The final step is to tabulate and graph each plan and compare their costs. From
Exhibit 19.5 we can see that using subcontractors resulted in the lowest cost (Plan 3).
Exhibit 19.6 shows the effects of the four plans. This is a cumulative graph illustrating the
expected results on the total production requirement.
KEY IDEA
In practice, there are
often many different
types of special
requirements. These
can be due to union
contracts, or other
factors relating to
worker availability, for
example.
498
Supply and Demand Planning and Control
Section 4
exhibit 19.4
Costs of Four Production Plans
Production Plan 1: Exact Production; Vary Workforce
January
February
Production requirement (from Exhibit 19.3)
1,850
1,425
1,000
850
1,150
1,725
Production hours required (Production
requirement × 5 hr/unit)
9,250
7,125
5,000
4,250
5,750
8,625
22
19
21
21
22
20
176
152
168
168
176
160
53
47
30
26
33
54
Working days per month
Hours per month per worker (Working
days × 8 hr/day)
Workers required (Production hours
required/Hours per month per worker)
New workers hired (assuming opening workforce equal to first month’s
requirement of 53 workers)
March
April
May
June
Total
0
0
0
0
7
21
$0
$0
$0
$0
$1,400
$4,200
0
6
17
4
0
0
Layoff cost (Workers laid off × $250)
$0
$1,500
$4,250
$1,000
$0
$0
$6,750
Straight-time cost (Production hours
required × $4)
$37,000
$28,500
$20,000
$17,000
$23,000
$34,500
Total cost
$160,000
$172,350
Hiring cost (New workers hired × $200)
Workers laid off
$5,600
Production Plan 2: Constant Workforce; Vary Inventory and Stock out
January
February
March
April
May
June
400
8
−276
−32
412
720
22
19
21
21
22
20
Production hours available (Working days
per month × 8 hr/day × 40 workers)*
7,040
6,080
6,720
6,720
7,040
6,400
Actual production (Production hours
available/5 hr/unit)
1,408
1,216
1,344
1,344
1,408
1,280
Demand forecast (from Exhibit 19.3)
1,800
1,500
1,100
900
1,100
1,600
400
Beginning inventory
Working days per month
Ending inventory (Beginning inventory +
Actual production − Demand forecast)
Shortage cost (Units short × $5)
Safety stock (from Exhibit 19.3)
Units excess (Ending inventory − Safety
stock) only if positive amount
Inventory cost (Units excess × $1.50)
Straight-time cost (Production hours
available × $4)
8
−276
−32
412
720
$0
$1,380
$160
$0
$0
$0
450
375
275
225
275
400
Total
$1,540
0
0
0
187
445
0
$0
$0
$0
$281
$668
$0
$948
$28,160
$24,320
$26,880
$26,880
$28,160
$25,600
$160,000
Total cost
$162,488
*(Sum of production requirement in Exhibit 19.3 × 5 hr/unit)/(Sum of production hours available × 8 hr/day) = (8,000 × 5)/(125 × 8) = 40.
Note that we have made one other assumption in this example: The plan can start with any
number of workers with no hiring or layoff cost. This usually is the case because an aggregate
plan draws on existing personnel, and we can start the plan that way. However, in an actual
application, the availability of existing personnel transferable from other areas of the firm may
change the assumptions.
Plan 1 is the “S” curve when we chase demand by varying workforce. Plan 2 has the highest average production rate (the line representing cumulative demand has the greatest slope).
Using subcontracting in Plan 3 results in it having the lowest production rate. Limits on the
amount of overtime available results in Plan 4 being similar to Plan 2.
Sales and Operations Planning
exhibit 19.4
499
Chapter 19
Costs of Four Production Plans (concluded)
Production Plan 3: Constant Low Workforce; Subcontract
January
February
March
May
June
1,850
1,425
1,000
22
19
21
850
1,150
1,725
21
22
20
Production hours available (Working
days × 8 hr/day × 25 workers)*
4,400
3,800
4,200
4,200
4,400
4,000
Actual production (Production hours
available/5 hr per unit)
880
760
840
840
880
800
Units subcontracted (Production
requirement − Actual production)
970
665
160
10
270
925
Subcontracting cost (Units subcontracted
× $20)
$19,400
$13,300
$3,200
$200
$5,400
$18,500
$60,000
Straight-time cost (Production hours
available × $4)
$17,600
$15,200
$16,800
$16,800
$17,600
$16,000
$100,000
Total cost
$160,000
Production requirement (from Exhibit 19.3)
Working days per month
April
Total
*Minimum production requirement. In this example, April is minimum of 850 units. Number of workers required for April is
(850 × 5)/(21 × 8) = 25.
Productio Plan 4: Constant Workforce Overtime
Beginning inventory
Working days per month
January
February
March
April
May
June
Total
400
0
0
177
554
792
22
19
21
21
22
20
Production hours available (Working days ×
8 hr/day × 38 workers)*
6,688
5,776
6,384
6,384
6,688
6,080
Regular shift production (Production hours
available/5 hr/unit)
1,338
1,155
1,277
1,277
1,338
1,216
Demand forecast (from Exhibit 19.3)
1,800
1,500
1,100
900
1,100
1,600
−62
−345
177
554
792
408
62
375
0
0
0
0
$1,860
$10,350
$0
$0
$0
$0
450
375
275
225
275
400
0
0
0
329
517
8
$0
$0
$0
$494
$776
$12
$1,281
$26,752
$23,104
$25,536
$25,536
$26,752
$24,320
$152,000
Total cost
$165,491
Units available before overtime (Beginning
inventory + Regular shift production −
Demand forecast). This number has been
rounded to the nearest integer.
Units overtime
Overtime cost (Units overtime × 5 hr/unit ×
$6/hr.)
Safety stock (from Exhibit 19.3)
Units excess (Units available before
overtime − Safety stock) only if positive
amount
Inventory cost (Units excessive × $1.50)
Straight-time cost (Production hours available × $4)
*Workers determined by trial and error. See text for explanation.
Each of these four plans focused on one particular cost, and the first three were simple pure
strategies. Obviously, there are many other feasible plans, some of which would use a combination of workforce changes, overtime, and subcontracting. The problems at the end of this
chapter include examples of such mixed strategies. In practice, the final plan chosen would
come from searching a variety of alternatives and future projections beyond the six-month
planning horizon we have used.
$12,210
500
Section 4
Supply and Demand Planning and Control
exhibit 19.5
Comparison of Four Plans
Plan 2: Constant
Workforce; Vary
Inventory and
Stock out
Plan 1: Exact
Production; Vary
Workforce
Costs
Hiring
$
5,600
Layoff
$
Plan 3: Constant
Low Workforce;
Subcontract
0
6,750
$
Plan 4: Constant
Workforce;
Overtime
0
$
0
0
0
0
Excess inventory
0
948
0
1,281
Shortage
0
1,540
0
0
Subcontract
0
0
60,000
0
Overtime
0
0
0
12,210
Straight time
exhibit 19.6
160,000
160,000
100,000
152,000
$172,350
$162,488
$160,000
$165,491
Four Plans for Satisfying a Production Requirement over the Number
of Production Days Available
8,000
7,600
Plan 2
7,000
6,400
6,000
Excess inventory (Plan 2)
5,600
5,200
5,000
Cumulative
number
of units
Shortage (Plan 2)
Cumulative
production
requirement
(also coincides
with Plan 1)
4,400
4,000
3,800
Plan 1
3,000
2,400
Plan 4
Overtime
(Plan 4)
Subcontracting (Plan 3)
2,000
1,800
Plan 3
1,400
1,000
5
15
25
35
45
55
65
75
85
95 105 115 125
Cumulative number of production days
Sales and Operations Planning
Chapter 19
501
Keep in mind that the cut-and-try approach does not guarantee finding the minimum-cost
solution. However, spreadsheet programs, such as Microsoft Excel, can perform cut-and-try
cost estimates in seconds and have elevated this kind of “what if” analysis to a fine art. More
sophisticated programs can generate much better solutions without the user having to intercede, as in the cut-and-try method.
A g g r e g a te Pla nning Ap p lie d to Services: Tu cso n Parks
an d Re cr e a tion D e pa r tme n t
Charting and graphic techniques are also useful for aggregate planning in service applications. The following example shows how a city’s parks and recreation department could use
the alternatives of full-time employees, part-time employees, and subcontracting to meet its
commitment to provide a service to the city.
Tucson Parks and Recreation Department has an operation and maintenance budget of
$9,760,000. The department is responsible for developing and maintaining open space, all
public recreational programs, adult sports leagues, golf courses, tennis courts, pools, and so
forth. There are 336 full-time-equivalent employees (FTEs). Of these, 216 are full-time permanent personnel who provide the administration and year-round maintenance to all areas.
The remaining 120 FTE positions are staffed with part-timers; about three-quarters of them
are used during the summer, and the remaining quarter in the fall, winter, and spring seasons.
The three-fourths (or 90 FTE positions) show up as approximately 800 part-time summer
jobs: lifeguards, baseball umpires, and instructors in summer programs for children. Eight
hundred part-time jobs came from 90 FTEs because many last only for a month or two, while
the FTE positions are a year long.
Currently, the only parks and recreation work subcontracted amounts to less than $100,000.
This is for the golf and tennis pros and for grounds maintenance at the libraries and veterans’
cemetery.
Because of the nature of city employment, the probable bad public image, and civil service
rules, the option to hire and fire full-time help daily or weekly to meet seasonal demand is
out of the question. However, temporary part-time help is authorized and traditional. Also,
it is virtually impossible to have regular (full-time) staff for all the summer jobs. During
the summer months, the approximately 800 part-time employees are staffing many programs
that occur simultaneously, prohibiting level scheduling over a normal 40-hour week. A wider
variety of skills are required (such as umpires, coaches, lifeguards, and teachers of ceramics,
guitar, karate, belly dancing, and yoga) than can be expected from full-time employees.
Three options are open to the department in its aggregate planning:
1.
2.
3.
The present method, which is to maintain a medium-level full-time staff and schedule
work during off-seasons (such as rebuilding baseball fields during the winter months)
and to use part-time help during peak demands.
Maintain a lower level of staff over the year and subcontract all additional work presently done by full-time staff (still using part-time help).
Maintain an administrative staff only and subcontract all work, including part-time
help. (This would entail contracts to landscaping firms and pool maintenance companies as well as to newly created private firms to employ and supply part-time help.)
The common unit of measure of work across all areas is full-time-equivalent jobs or
employees. For example, assume in the same week that 30 lifeguards worked 20 hours each,
40 instructors worked 15 hours each, and 35 baseball umpires worked 10 hours each. This is
equivalent to (30 × 20) + (40 × 15) + (35 × 10) = 1,550 ÷ 40 = 38.75 FTE positions for that
week. Although a considerable amount of workload can be shifted to off-season, most of the
work must be done when required.
Full-time employees consist of three groups: (1) the skeleton group of key department
personnel coordinating with the city, setting policy, determining budgets, measuring performance, and so forth; (2) the administrative group of supervisory and office personnel who
are responsible for or whose jobs are directly linked to the direct-labor workers; and (3) the
KEY IDEA
With services, inventory
is typically not an issue.
Sometimes a few extra
employees are added
as a buffer to cover
employee vacations
and other needs.
502
Supply and Demand Planning and Control
Section 4
direct-labor workforce of 116 full-time positions. These workers physically maintain the
department’s areas of responsibility, such as cleaning up, mowing golf greens and ballfields,
trimming trees, and watering grass.
Cost information needed to determine the best alternative strategy is
Full-time direct-labor employees
Average wage rate
$8.90 per hour
Fringe benefits
17% of wage rate
Administrative costs
20% of wage rate
Part-time employees
Average wage rate
$8.06 per hour
Fringe benefits
11% of wage rate
Administrative costs
25% of wage rate
Subcontracting all full-time jobs
$3.2 million
Subcontracting all part-time jobs
$3.7 million
June and July are the peak demand seasons in Tucson. Exhibit 19.7 shows the high requirements for June and July personnel. The part-time help reaches 576 FTE positions (although,
in actual numbers, this is approximately 800 different employees). After a low fall and winter
staffing level, the demand shown as “full-time direct” reaches 130 in March (when grounds
are reseeded and fertilized) and then increases to a high of 325 in July. The present method
levels this uneven demand over the year to an average of 116 full-time year-round employees
by early scheduling of work. Note that the actual requirement is 115 (28,897/252 = 114.67),
but an extra employee has been added as a safety measure. As previously mentioned, no
attempt is made to hire and lay off full-time workers to meet this uneven demand.
Exhibit 19.8 shows the cost calculations for all three alternatives and compares the total
costs for each alternative. From this analysis, it appears that the department is already using
the lowest-cost alternative (Alternative 1).
exhibit 19.7
Actual Demand Requirement for Full-Time Direct Employees and Full-Time-Equivalent (FTE)
Part-Time Employees
Jan.
Days
Full-time employees
Full-time days*
Full-time-equivalent
part-time employees
FTE days
22
Feb.
20
Mar.
Apr.
21
May
22
June
21
July
20
21
Aug.
21
Sept.
21
Oct.
23
Nov.
18
Dec.
Total
22
66
28
130
90
195
290
325
92
45
32
29
60
1,452
560
2,730
1,980
4,095
5,800
6,825
1,932
945
736
522
1,320
41
75
72
68
72
302
576
72
0
68
84
27
902
1,500
1,512
1,496
1,512
6,040
12,096
1,512
0
1,564
1,512
594
252
28,897
30,240
*Full-time days are derived by multiplying the number of days in each month by the number of workers.
600
500
FTE part-time
400
Full-timeequivalent
300
employees
required
200
Full-time
100
Jan.
Feb. Mar. Apr. May June
July Aug. Sept. Oct. Nov. Dec.
Sales and Operations Planning
503
Chapter 19
Three Possible Plans for the Parks and Recreation Department
exhibit 19.8
Alternative 1: Maintain 116 full-time regular direct workers. Schedule work during off-seasons to level workload
throughout the year. Continue to use 120 full-time-equivalent (FTE) part-time employees to meet high demand periods.
Days per Year
(Exhibit 19.7)
Hours
(Employees × Days
× 8 Hours)
Wages
(Full-Time, $8.90;
Part-Time, $8.06)
Fringe Benefits
(Full-Time, 17%;
Part-Time, 11%)
Administrative Cost
(Full-Time, 20%;
Part-Time, 25%)
116 full-time regular
employees
252
233,856
$2,081,318
$353,824
$416,264
120 part-time
employees
252
241,920
$1,949,875
$214,486
$487,469
$4,031,193
$568,310
$903,733
Costs
Total cost = $5,503,236
Alternative 2: Maintain 50 full-time regular direct workers and the present 120 FTE part-time employees. Subcontract jobs, releasing 66
full-time regular employees. Subcontract cost, $2,200,000.
Cost
Days per Year
(Exhibit 19.7)
Hours
(Employees ×
Days × 8 Hours)
Wages
(Full-Time, $8.90;
Part-Time, $8.06)
Fringe Benefits
(Full-Time, 17%;
Part-Time, 11%)
Administrative Cost
(Full-Time, 20%;
Part-Time, 25%)
50 full-time
employees
252
100,800
$
897,120
$152,510
$179,424
120 FTE part-time
employees
252
241,920
$1,949,875
$214,486
$487,469
$2,846,995
$366,996
$666,893
Subcontracting
cost
Subcontract
Cost
$2,200,000
Total cost = $6,080,884
$2,200,000
Alternative 3: Subcontract all jobs previously performed by 116 full-time regular employees. Subcontract cost $3,200,000. Subcontract
all jobs previously performed by 120 FTE part-time employees. Subcontract cost $3,700,000.
Cost
Subcontract
Cost
0 full-time employees
0 part-time employees
Subcontract full-time jobs
$3,200,000
Subcontract part-time jobs
$3,700,000
Total cost
$6,900,000
LO 19–3
Explain yield management
and why it is an important
strategy.
YIELD MANAGEMENT
Why is it that the guy sitting next to you on the plane paid half the price you paid for your
ticket? Why was a hotel room you booked more expensive when you booked it six months in
advance than when you checked in without a reservation (or vice versa)? The answers lie in
the practice known as yield management. Yield management can be defined as the process
of allocating the right type of capacity to the right type of customer at the right price and
time to maximize revenue or yield. Yield management can be a powerful approach to making
demand more predictable, which is important to aggregate planning.
Yield management
Given limited capacity, the
process of allocating it
to customers at the right
price and time to maximize
profit.
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Yield management has existed as long as there
has been limited capacity for serving customers.
However, its widespread scientific application
began with American Airlines’ computerized
reservation system (SABRE), introduced in
the mid-1980s. The system allowed the airline
to change ticket prices on any routes instantaneously as a function of forecast demand. People
Express, a no-frills, low-cost competitor airline,
was one of the most famous victims of American’s yield management system. Basically, the
system enabled hour-by-hour updating on competing routes so that American could match or
better prices wherever People Express was flying. The president of People Express realized
that the game was lost when his mother flew on
Many Hotel Chains Use Priceline to Sell Excess Capacity at a Discount.
American to People’s hub for a lower price than
© NetPhotos/Alamy
People could offer!
From an operational perspective, yield management is most effective when
1.
2.
3.
4.
5.
Demand can be segmented by customer.
Fixed costs are high and variable costs are low.
Inventory is perishable.
Product can be sold in advance.
Demand is highly variable.
Hotels illustrate these five characteristics well. They offer one set of rates during the week
for the business traveler and another set during the weekend for the vacationer. The variable
costs associated with a room (such as cleaning) are low in comparison to the cost of adding
rooms to the property. Available rooms cannot be transferred from night to night, and blocks
of rooms can be sold to conventions or tours. Finally, potential guests may cut short their stay
or not show up at all.
Most organizations (such as airlines, rental car agencies, cruise lines, and hotels) manage yield by establishing decision rules for opening or closing rate classes as a function of
expected demand and available supply. The methodologies for doing this can be quite sophisticated. A common approach is to forecast demand over the planning horizon and then use
marginal analysis to determine the rates that will be charged if demand is forecast as being
above or below set control limits around the forecast mean.
Ope r a ting Yield Man agemen t Syst ems
A number of interesting issues arise in managing yield. One is that pricing structures must
appear logical to the customer and justify the different prices. Such justification, commonly
called rate fences, may have either a physical basis (such as a room with a view) or a nonphysical basis (like unrestricted access to the Internet). Pricing also should relate to addressing specific capacity problems. If capacity is sufficient for peak demand, price reductions to
stimulate off-peak demand should be the focus. If capacity is insufficient, offering deals to
customers who arrive during non-peak periods (or creating alternative service locations) may
enhance revenue generation.
A second issue is handling variability in arrival or starting times, duration, and time
between customers. This entails employing maximally accurate forecasting methods (the
greater the accuracy in forecasting demand, the more likely yield management will succeed);
coordinated policies on overbooking, deposits, and no-show or cancellation penalties; and
well-designed service processes that are reliable and consistent.
A third issue relates to managing the service process. Some strategies include scheduling additional personnel to meet peak demand, increasing customer self-service, creating
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adjustable capacity, utilizing idle capacity for complementary services, and cross-training
employees to create reserves for peak periods.
The fourth and perhaps most critical issue is training workers and managers to work in
an environment where overbooking and price changes are standard occurrences that directly
impact the customer. Companies have developed creative ways of mollifying overbooked customers. A golf course company offers $100 putters to players who have been overbooked at
a popular tee time. Airlines, of course, frequently give overbooked passengers free tickets for
other flights.
Concept Connections
LO 19–1 Understand what sales and operations planning is and how it coordinates
manufacturing, logistics, service, and marketing plans.
Summary
∙ The output of the sales and operation planning process
is the aggregate plan.
∙ The aggregate plan is a high-level operational plan
that can be executed by the operations and supply
chain functions.
∙ The process brings together marketing and sales, distribution and logistics, operations, finance, and product development to agree on the best plan to match
supply with demand.
∙ The input into the process is the sales plan developed
by marketing.
∙ Typically, aggregation is done by product families and
by groups of customers, and the plan is completed
using these aggregate supply and demand quantities.
∙ Outputs of the plan are planned production rates,
aggregate labor requirements, and expected finished
good levels.
∙ Cost minimization is typically a major driver when
finding a plan.
Key Terms
Aggregate operations plan A plan for labor and pro-
duction for the intermediate term with the objective to
minimize the cost of resources needed to meet demand.
Sales and operations planning The process that companies use to keep demand and supply in balance by
coordinating manufacturing, distribution, marketing, and
financial plans.
Long-range planning One year or more.
Intermediate-range planning Involves a time period of
usually 3 to 18 months.
Short-range planning From a day to six months.
Production rate Number of units completed per unit of time.
Workforce level Number of workers needed in a period.
Inventory on hand Inventory carried from the previous
period.
Production planning strategies Plans for meeting
demand that involve trade-offs in the number of workers
employed, work hours, inventory, and shortages.
Pure strategy A simple strategy that uses just one option,
such as hiring and firing workers, for meeting demand.
Mixed strategy A more complex strategy that combines
options for meeting demand.
LO 19–2 Construct and evaluate aggregate plans that employ different strategies for meeting
demand.
Summary
∙ Companies commonly use simple cut-and-try
(trial-and-error) techniques for analyzing aggregate
planning problems. Sophisticated mathematical programming techniques can also be used.
∙ Strategies vary greatly depending on the situation faced
by the company. Plans are typically evaluated based on
cost, but it is important to consider the feasibility of the
plan (that overtime is not excessive, for example).
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LO 19–3 Explain yield management and why it is an important strategy.
Summary
∙ Yield management occurs when a firm adjusts the
price of its product or service in order to influence
demand. Usually, it is done to make future demand
more predictable, which is important to successful
sales and operations planning.
∙ This practice is commonly used in the airline, hotel,
casino, and auto retail industries, for example.
∙ Policies that involve overbooking, requiring deposits,
and no-show or cancellation penalties are coordinated
with the different pricing scheme.
Key Term
Yield management Given limited capacity, the process
of allocating it to customers at the right price and time to
maximize profit.
Solved Problem
LO19–2 Jason Enterprises (JE) produces video telephones for the home market. Quality is not quite
as good as it could be at this point, but the selling price is low and Jason can study market
response while spending more time on R&D.
At this stage, however, JE needs to develop an aggregate production plan for the six
months from January through June. You have been commissioned to create the plan. The following information should help.
Demand and Working Days
January
February
March
April
May
June
Totals
500
600
650
800
900
800
4,250
22
19
21
21
22
20
125
Demand forecast
Number of working days
Costs
Materials
Inventory holding cost
Marginal cost of stock out
Marginal cost of subcontracting
Hiring and training cost
Layoff cost
Labor hours required
$100.00/unit
$10.00/unit/month
$20.00/unit/month
$100.00/unit ($200 subcontracting cost
less $100 material savings)
$50.00/worker
$100.00/worker
4/unit
Straight-time cost (first eight hours each day)
$12.50/hour
Overtime cost (time and a half)
$18.75/hour
Inventory
Beginning inventory
Safety stock required
200 units
0% of month demand
What is the cost of each of the following production strategies?
a. Produce exactly to meet demand; vary workforce (assuming opening workforce equal to
first month’s requirements).
b. Constant workforce; vary inventory and allow shortages only (assuming a workforce of
10).
c. Constant workforce of 10; use subcontracting.
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Solution
Aggregate Production Planning Requirements
January
February
March
April
May
June
Beginning inventory
200
0
0
0
0
0
Demand forecast
500
600
650
800
900
800
0
0
0
0
0
0
300
600
650
800
900
800
0
0
0
0
0
0
Safety stock (0.0 ×
Demand forecast)
Production requirement
(Demand forecast +
Safety stock – Beginning
inventory)
Ending inventory (Beginning
inventory + Production
requirement – Demand
forecast)
Total
Production Plan 1: Exact Production; Vary Workforce
January February
Production requirement
Production hours required
(Production requirement ×
4 hr/unit)
March
April
May
June
300
600
650
800
900
800
1,200
2,400
2,600
3,200
3,600
3,200
Working days per month
22
19
21
21
22
20
Hours per month per
worker (Working days ×
8 hr/day)
176
152
168
168
176
160
Workers required
(Production hours
required/Hours per
month per worker)
7
16
15
19
20
20
New workers hired
(assuming opening
workforce equal to first
month’s requirement of
7 workers)
0
9
0
4
1
0
Hiring cost (New workers
hired × $50)
$0
$450
$0
$200
$50
$0
0
0
1
0
0
0
$0
$0
$100
$0
$0
$0
$15,000
$30,000
$32,500
$40,000
$45,000
Workers laid off
Layoff cost (Workers
laid off × $100)
Straight-time cost
(Production hours
required × $12.50)
Total
$700
$100
$40,000 $202,500
Total cost $203,300
Production Plan 2: Constant Workforce; Vary Inventory and Stock Out
January February
Beginning inventory
Working days per month
Production hours available (Working days per
month × 8 hr/day × 10
workers)*
March
April
May
June
200
140
–80
–310
–690
–1150
22
19
21
21
22
20
1,760
1,520
1,680
1,680
1,760
1,600
*Assume a constant workforce of 10.
Total
(continued)
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Production Plan 2: Constant Workforce; Vary Inventory and Stock Out
January February
March
April
May
June
Actual production
(Production hours
available/4 hr/unit)
440
380
420
420
440
400
Demand forecast
500
600
650
800
900
800
Ending inventory
(Beginning inventory
+ Actual production –
Demand forecast)
140
–80
–310
–690
–1,150
–1,550
$0
$1,600
$6,200
$13,800
$23,000
$31,000
0
0
0
0
0
0
Shortage cost (Units
short × $20)
Safety stock
Units excess (Ending
inventory – Safety
stock; only if positive
amount)
Total
$75,600
140
0
0
0
0
0
Inventory cost (Units
excess × $10)
$1,400
$0
$0
$0
$0
$0
$1,400
Straight-time cost
(Production hours
available × $12.50)
$22,000
$19,000
$21,000
$21,000
$22,000
$20,000
$125,000
Total cost $202,000
Production Plan 3: Constant Workforce; Subcontract
January
February
Production requirement
Working days per month
March
April
May
June
300
†
460
650
800
900
800
22
19
21
21
22
20
1,760
1,520
1,680
1,680
1,760
1,600
440
380
420
420
440
400
Units subcontracted
(Production requirements –
Actual production)
0
80
230
380
460
400
Subcontracting cost (Units
subcontracted × $100)
$0
Production hours available
(Working days × 8 hr/day ×
10 workers)*
Actual production
(Production hours
available/4 hrs per unit)
Straight-time cost
(Production hours
available × $12.50)
Total
$8,000 $23,000 $38,000 $46,000 $40,000 $155,000
$22,000 $19,000
$21,000 $21,000 $22,000 $20,000 $125,000
Total cost $280,000
*Assume a constant workforce of 10.
†
600 – 140 units of beginning inventory in February.
Summary
Plan Description
Hiring
Layoff
1. Exact production;
vary workforce
$700
$100
Subcontract
Shortage
Excess
Inventory
$202,500
2. Constant workforce;
vary inventory and
shortages
3. Constant workforce;
subcontract
Straight
Time
$125,000
$155,000
$125,000
Total
Cost
$203,300
$75,600
$1,400
$202,000
$280,000
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Discussion Questions
LO19–1
LO19–2
LO19–3
1. What are the basic controllable variables of a production planning problem? What are the
four major costs?
2. Distinguish between pure and mixed strategies in production planning.
3. What are the major differences between aggregate planning in manufacturing and aggregate planning in services?
4. How does forecast accuracy relate, in general, to the practical application of the aggregate
planning models discussed in the chapter?
5. In what way does the time horizon chosen for an aggregate plan determine whether it is the
best plan for the firm?
6. Define yield management. How does it differ from the pure strategies in production
planning?
7. How would you apply yield management concepts to a barbershop? A soft drink vending
machine?
Objective Questions
LO19–1
LO19–2
1. Major operations and supply planning activities can be grouped into categories based on
the relevant time range of the activity. Into what time range category does sales and operations planning fit?
2. What category of planning covers a period from a day to six months, with daily or weekly
time increments?
3. In the agriculture industry, migrant workers are commonly employed to pick crops ready
for harvest. They are hired as needed and are laid off once the crops are picked. The realities of the industry make this approach necessary. Which production planning strategy best
describes this approach?
4. What is the term for a more complex production strategy that combines approaches from
more than one basic strategy?
5. List at least three of the four costs relevant to the aggregate production plan.
6. Which of the four costs relevant to aggregate production planning is the most difficult to
accurately measure?
7. Develop a production plan and calculate the annual cost for a firm whose demand forecast is
fall, 10,000; winter, 8,000; spring, 7,000; summer, 12,000. Inventory at the beginning of fall is
500 units. At the beginning of fall, you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition,
you have negotiated with the union an option to use the regular workforce on overtime during
winter or spring if overtime is necessary to prevent stock outs at the end of those quarters.
Overtime is not available during the fall. Relevant costs are hiring, $100 for each temp; layoff,
$200 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit;
straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per
worker hour, with eight hours per day and 60 days per season. (Answer in Appendix D)
8. Plan production for a four-month period: February through May. For February and March,
you should produce to exact demand forecast. For April and May, you should use overtime
and inventory with a stable workforce; stable means that the number of workers needed for
March will be held constant through May. However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May (zero overtime in
February and March). If demand exceeds supply, then backorders occur. There are 100
workers on January 31. You are given the following demand forecast: February, 80,000;
March, 64,000; April, 100,000; May, 40,000. Productivity is four units per worker hour,
eight hours per day, 20 days per month. Assume zero inventory on February 1. Costs are:
hiring, $50 per new worker; layoff, $70 per worker laid off; inventory holding, $10 per
unit-month; straight-time labor, $10 per hour; overtime, $15 per hour; backorder, $20 per
unit. Find the total cost of this plan.
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9. Plan production for the next year. The demand forecast is: spring, 20,000; summer, 10,000;
fall, 15,000; winter, 18,000. At the beginning of spring you have 70 workers and 1,000
units in inventory. The union contract specifies that you may lay off workers only once a
year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning of
summer and the number hired at the start of fall should result in planned production levels
for summer and fall that equal the demand forecasts for summer and fall, respectively. If
demand exceeds supply, use overtime in spring only, which means that backorders could
occur in winter. You are given these costs: hiring, $100 per new worker; layoff, $200 per
worker laid off; holding, $20 per unit-quarter; backorder cost, $8 per unit; straight-time
labor, $10 per hour; overtime, $15 per hour. Productivity is 0.5 unit per worker hour, eight
hours per day, 50 days per quarter. Find the total cost.
10. DAT, Inc., needs to develop an aggregate plan for its product line. Relevant data are
Production time
1 hour per unit
Beginning inventory
500 units
Average labor
cost
$10 per hour
Safety stock
One-half month
Workweek
5 days, 8 hours
each day
Shortage cost
$20 per unit per
month
Days per month
Assume 20 workdays
per month
Carrying cost
$5 per unit per
month
The forecast for next year is
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
2,500
3,000
4,000
3,500
3,500
3,000
3,000
4,000
4,000
4,000
3,000
3,000
Management prefers to keep a constant workforce and production level, absorbing
variations in demand through inventory excesses and shortages. Demand not met is carried over to the following month.
Develop an aggregate plan that will meet the demand and other conditions of the problem.
Do not try to find the optimum; just find a good solution and state the procedure you might
use to test for a better solution. Make any necessary assumptions. (Answer in Appendix D)
11. Old Pueblo Engineering Contractors creates six-month “rolling” schedules, which are
recomputed monthly. For competitive reasons (it would need to divulge proprietary design
criteria, methods, and so on), Old Pueblo does not subcontract. Therefore, its only options
to meet customer requirements are (1) work on regular time; (2) work on overtime, which
is limited to 30 percent of regular time; (3) do customers’ work early, which would cost
an additional $5 per hour per month; and (4) perform customers’ work late, which would
cost an additional $10 per hour per month penalty, as provided by their contract.
Old Pueblo has 25 engineers on its staff at an hourly rate of $30. The overtime rate is
$45. Customers’ hourly requirements for the six months from January to June are
January
5,000
February
March
April
May
June
4,000
6,000
6,000
5,000
4,000
Develop an aggregate plan using a spreadsheet. Assume 20 working days in each month.
12. Alan Industries is expanding its product line to include three new products: A, B, and C.
These are to be produced on the same production equipment, and the objective is to meet
the demands for the three products using overtime where necessary. The demand forecast
for the next four months, in hours required to make each product, is
Product
April
May
June
July
A
800
600
800
1,200
B
600
700
900
1,100
C
700
500
700
850
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Because the products deteriorate rapidly, there is a high loss in quality and, consequently,
a high carrying cost when a product is made and carried in inventory to meet future
demand. Each hour’s production carried into future months costs $3 per production hour
for A, $4 for Model B, and $5 for Model C.
Production can take place either during regular working hours or during overtime.
Regular time is paid at $4 when working on A, $5 for B, and $6 for C. The overtime premium is 50 percent of the regular time cost per hour.
The number of production hours available for regular time and overtime is
Regular time
Overtime
April
May
June
July
1,500
700
1,300
650
1,800
900
2,000
1,000
Set up the problem in a spreadsheet and an optimal solution using the Excel Solver.
Appendix A describes how to use the Excel Solver.
13. Shoney Video Concepts produces a line of video streaming servers that are linked to computers for storing movies. These devices have very fast access and large storage capacity.
Shoney is trying to determine a production plan for the next 12 months. The main
criterion for this plan is that the employment level is to be held constant over the period.
Shoney is continuing in its R&D efforts to develop new applications and prefers not to
cause any adverse feelings with the local workforce. For the same reason, all employees
should put in full workweeks, even if that is not the lowest-cost alternative. The forecast
for servers for the next 12 months is
Month
January
February
March
April
May
June
Forecast Demand
600
800
900
600
400
300
Month
July
August
September
October
November
December
Forecast Demand
200
200
300
700
800
900
Manufacturing cost is $200 per server, equally divided between materials and labor.
Inventory storage cost is $5 per month. A shortage of servers results in lost sales and is
estimated to cost an overall $20 per unit short.
The inventory on hand at the beginning of the planning period is 200 units. Ten labor
hours are required per DVD player. The workday is eight hours.
Develop an aggregate production schedule for the year using a constant workforce. For
simplicity, assume 22 working days each month except July, when the plant closes down
for three weeks’ vacation (leaving seven working days). Assume that total production
capacity is greater than or equal to total demand.
14. Develop a production schedule to produce the exact production requirements by varying
the workforce size for the following problem. Use the example in the chapter as a guide
(Plan 1).
The monthly forecasts for Product X for January, February, and March are 1,000,
1,500, and 1,200, respectively. Safety stock policy recommends that half of the forecast
for that month be defined as safety stock. There are 22 working days in January, 19 in
February, and 21 in March. Beginning inventory is 500 units.
Manufacturing cost is $200 per unit, storage cost is $3 per unit per month, standard
pay rate is $6 per hour, overtime rate is $9 per hour, cost of stock out is $10 per unit per
month, marginal cost of subcontracting is $10 per unit, hiring and training cost is $200
per worker, layoff cost is $300 per worker, and worker productivity is 0.1 unit per hour.
Assume that you start off with 50 workers and that they work 8 hours per day.
15. Helter Industries, a company that produces a line of women’s bathing suits, hires temporaries to help produce its summer product demand. For the current four-month rolling
schedule, there are three temps on staff and 12 full-time employees. The temps can be
hired when needed and can be used as needed, whereas the full-time employees must
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be paid whether they are needed or not. Each full-time employee can produce 205 suits,
while each temporary employee can produce 165 suits per month.
Demand for bathing suits for the next four months is as follows:
LO19–3
May
June
July
August
3,200
2,800
3,100
3,000
Beginning inventory in May is 403 bathing suits. Bathing suits cost $40 to produce and
carrying cost is 24 percent per year.
Develop an aggregate plan that uses the 12 full-time employees each month and a
minimum number of temporary employees. Assume that all employees will produce at
their full potential each month. Calculate the inventory carrying cost associated with your
plan using planned end of month levels.
16. The widespread scientific application of yield management began within what industry?
17. Under what type of demand is yield management most effective?
18. In a yield managment system, pricing differences must appear logical and justified to the
customer. What is the basis for this justification commonly called?
19. The essence of yield management is the ability to manage what?
Analytics Exercise: Developing an Aggregate Plan—Bradford Manufacturing
The Situation
You are the operations manager for a manufacturing plant
that produces pudding food products. One of your important responsibilities is to prepare an aggregate plan for the
plant. This plan is an important input into the annual budget process. The plan provides information on production
rates, manufacturing labor requirements, and projected
finished goods inventory levels for the next year.
You make those little boxes of pudding mix on packaging lines in your plant. A packaging line has a number
of machines that are linked by conveyors. At the start of
the line, the pudding is mixed; it is then placed in small
packets. These packets are inserted into the small pudding
boxes, which are collected and placed in cases that hold 48
boxes of pudding. Finally, 160 cases are collected and put
on a pallet. The pallets are staged in a shipping area from
which they are sent to four distribution centers. Over the
years, the technology of the packaging lines has improved
so that all the different flavors can be made in relatively
small batches with no setup time to switch between flavors.
The plant has 15 of these lines, but currently only 10 are
being used. Six employees are required to run each line.
The demand for this product fluctuates from month
to month. In addition, there is a seasonal component, with
peak sales before Thanksgiving, Christmas, and Easter
each year. To complicate matters, at the end of the first
quarter of each year the marketing group runs a promotion in which special deals are made for large purchases.
Business is going well, and the company has been experiencing a general increase in sales.
The plant sends product to four large distribution
warehouses strategically located in the United States.
Trucks move product daily. The amounts shipped are
based on maintaining target inventory levels at the warehouses. These targets are calculated based on anticipated
weeks of supply at each warehouse. Current targets are
set at two weeks of supply.
In the past, the company has had a policy of producing very close to what it expects sales to be because of
limited capacity for storing finished goods. Production
capacity has been adequate to support this policy.
A sales forecast for next year has been prepared by
the marketing department. The forecast is based on quarterly sales quotas, which are used to set up an incentive
program for the salespeople. Sales are mainly to the large
U.S. retail grocers. The pudding is shipped to the grocers
from the distribution warehouses based on orders taken
by the salespeople.
Your immediate task is to prepare
an aggregate plan for the coming year.
The technical and economic factors
that must be considered in this plan are
shown next.
3,000
Forecast Demand by Quarter (1,000 Case Units)
2,500
2,000
1,500
1,000
500
0
1st
(1–13)
2nd
(14–26)
3rd
(27–39)
4th
1st
(40–52) (Next Year)
Sales and Operations Planning
Technical and Economic Information
1. The plant runs 5 days each week, and currently is
running 10 lines with no overtime. Each line requires
six people to run. For planning purposes, the lines
are run for 7.5 hours each normal shift. Employees,
though, are paid for eight hours’ work. It is possible
to run up to two hours of overtime each day, but it
must be scheduled for a week at a time, and all the
lines must run overtime when it is scheduled. Workers are paid $20.00/hour during a regular shift and
$30.00/hour on overtime. The standard production
rate for each line is 450 cases/hour.
2. The marketing forecast for demand is as follows:
Q1—2,000; Q2—2,200; Q3—2,500; Q4—2,650;
and Q1 (next year)—2,200. These numbers are
in 1,000-case units. Each number represents a
13-week forecast.
3. Management has instructed manufacturing to
maintain a two-week safety stock supply of pudding inventory in the warehouses. The two-week
supply should be based on future expected sales.
The following are ending inventory target levels to
comply with the safety stock requirement for each
quarter: Q1—338; Q2—385; Q3—408; Q4—338.
4. Inventory carrying cost is estimated by accounting
to be $1.00 per case per year. This means that if a
case of pudding is held in inventory for an entire year,
the cost to just carry that case in inventory is $1.00.
If a case is carried for only one week, the cost is
$1.00/52, or $0.01923. The cost is proportional to the
time carried in inventory. There are 200,000 cases in
inventory at the beginning of Q1 (this is 200 cases in
the 1,000-case units that the forecast is given in).
5. If a stock out occurs, the item is backordered and
shipped at a later date. The cost when a backorder
occurs is $2.40 per case due to the loss of goodwill
and the high cost of emergency shipping.
6. The human resource group estimates that it costs
$5,000 to hire and train a new production employee.
It costs $3,000 to lay off a production worker.
Chapter 19
513
7. Make the following assumptions in your cost
calculations:
∙ Inventory costs are based on inventory in excess
of the safety stock requirement.
∙ Backorder costs are incurred on the negative
deviation from the planned safety stock requirement, even though planned inventory may be
positive.
∙ Overtime must be used over an entire quarter
and should be based on hours per day over that
time.
Questions
1. Prepare an aggregate plan for the
coming year, assuming that the sales
forecast is perfect. Use the worksheet “Bradford Manufacturing”
that is in the “19 Sales and Operations Planning” spreadsheet. In the
worksheet, an area has been designated for your
aggregate plan solution. Supply the number of
packaging lines to run and the number of overtime
hours for each quarter. You will need to set up the
cost calculations in the spreadsheet.
You may want to try using the Excel Solver to
find a low-cost solution. Remember that your final
solution needs an integer number of lines and an
integer number of overtime hours for each quarter. (Solutions that require 8.9134 lines and 1.256
hours of overtime are not feasible.)
It is important that your spreadsheet calculations are set up so that any values in the number of
lines and overtime hours rows evaluates correctly.
Your spreadsheet will be evaluated based on this.
2. Find a solution to the problem that goes beyond
just minimizing cost. Prepare a short write-up that
describes the process you went through to find
your solution and that justifies why you think it is a
good solution.
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. Term used to refer to the process a firm uses to balance supply and demand.
2. When doing aggregate planning, these are the three
general operations–related variables that can be
adjusted.
3. A strategy where the production rate is set to match
expected demand.
4. When overtime is used to meet demand and avoid the
costs associated with hiring and firing.
5. A strategy that uses inventory and backorders as part
of the strategy to meet demand.
6. Sometimes a firm may choose to have all or part of the
work done by an outside vendor. This is the term used
for the approach.
7. If expected demand during the next four quarters
is 150, 125, 100, and 75 thousand units, and each
514
Section 4
Supply and Demand Planning and Control
worker can produce 1,000 units per quarter, how many
workers should be used if a level strategy is being
employed?
8. Given the data from question 7, how many workers
would be needed for a chase strategy?
9. In a service setting, what general operations–related
variable is not available compared to a production
setting?
10. The practice of allocating capacity and manipulating
demand to make it more predictable.
Answers to Practice Exam 1. Sales and operations planning 2. Production rate, workforce level, inventory 3. Chase 4. Stable workforce – Variable
work hours 5. Level strategy 6. Subcontracting 7. 113 8. 150, 125, 100, 75 9. Inventory 10. Yield management
20
Inventory
Management
Learning Objectives
LO 20–1 Explain how inventory is used and understand what it costs.
LO 20–2 Analyze how different inventory control systems work.
LO 20–3 Analyze inventory using the Pareto principle.
W I LL WAREHOUSES BE NEEDED IN THE
FUTURE?
Logistics visionaries have talked for years about eliminating—or at least drastically
reducing—the role of inventory in modern supply chains. The most efficient, slackfree supply chains, after all, wouldn’t require any inventory buffer because supply and
demand would be in perfect sync. This vision certainly has its appeal: The death of
inventory would mean dramatically reduced logistics costs and simplified fulfillment.
There’s no need to write a eulogy for inventory just yet. Most
companies haven’t honed their networks and technologies well
enough to eliminate the need for at least minimal inventory. Logistics managers have to perform a daily, delicate act balancing:
•
•
•
•
Transportation costs against fulfillment speed
Inventory costs against the cost of stock outs
Customer satisfaction against the cost to serve
New capabilities against profitability
What’s more, two accelerating business trends are making it
even harder to synchronize supply chains.
First, global sourcing is forcing supply chains to stretch farther
across borders. The goods people consume are increasingly made
in some other part of the world, particularly in Asia. This acceleration in global sourcing changes the logistics equation. When goods
cross borders, considerations such as fulfillment speed (these are
the activities performed once an order is received) and inventory
costs get more complicated. Second, powerful retailers and other
end customers with clout are starting to push value-added supply
chain responsibilities further up the supply chain. More customers
are asking manufacturers or third-party logistics providers to label
© Daniel Acker/Bloomberg via Getty Images
515
and prepare individual items so the products are ready to go directly to store shelves.
With added responsibilities, of course, come added costs. Upstream suppliers are
always looking for ways to squeeze more costs out of other areas of the supply chain,
such as transportation and distribution.
A growing number of companies are overcoming these barriers by taking a more
direct approach to global fulfillment. This direct-to-store approach—also known as
distribution center bypass or direct distribution—keeps inventory moving from manufacturer to end customer by eliminating stops at warehouses along the way. Because
companies can shrink the fulfillment cycle and eliminate inventory costs, direct-tostore can offer a good balance between fulfillment speed and logistics costs.
Internet-enabled electronic links between supply chain partners have allowed better coordination and collaboration among the various supply chain segments. Meanwhile, at the front of the supply chain, increasingly sophisticated point-of-sale systems
can capture product demand patterns. This information can then be fed up the supply
chain to manufacturers and components suppliers. More accurate sales-forecasting
tools take some of the guesswork out of production and reduce the need for large
inventory safety stocks. Tracking and tracing tools are also available to follow orders
across borders and through the hands of different supply partners.
In short, companies no longer need as much inventory gathering dust in warehouses because they can better synchronize production and distribution with
demand. Direct-to-store lets them keep inventory in motion—across borders and
around the world.
You should visualize inventory as stacks of money sitting on forklifts, on shelves, and in
trucks and planes while in transit. That’s what inventory is—money. For many businesses,
inventory is the largest asset on the balance sheet at any given time, even though it is often not
very liquid. It is a good idea to try to get your inventory down as far as possible.
The economic benefit from inventory reduction is evident from the following statistics:
The average cost of inventory in the United States is 30 to 35 percent of its value. For example, if a firm carries an inventory of $20 million, it costs the firm more than $6 million per
year. These costs are due mainly to obsolescence, insurance, and opportunity costs. If the
amount of inventory could be reduced to $10 million, for instance, the firm would save over
$3 million, which goes directly to the bottom line; that is, the savings from reduced inventory
results in increased profit.
UNDER STANDING INVENTORY MANAGEMENT
LO 20–1
Explain how inventory is
used and understand what
it costs.
516
This chapter and Chapter 21 present techniques designed to manage inventory in different
supply chain settings. In this chapter, the focus is on settings where the desire is to maintain
a stock of inventory that can be delivered to our customers on demand. Recall in C
­ hapter 7
the concept of the customer order decoupling point, which is a point where inventory is
positioned to allow processes or entities in the supply chain to operate independently. For
­example, if a product is stocked at a retailer, the customer pulls the item from the shelf and the
manufacturer never sees a customer order. In this case, inventory acts as a buffer to separate
the customer from the manufacturing process. Selection of decoupling points is a strategic
decision that determines customer lead times and can greatly impact inventory investment.
The closer this point is to the customer, the quicker the customer can be served.
Inventory Management
Chapter 20
The techniques described in this chapter are suited for managing the inventory at these decoupling points. Typically, there is a trade-off where quicker response to customer demand comes
at the expense of greater inventory investment. This is because finished goods inventory is more
expensive than raw material inventory. In practice, the idea of a single decoupling point in a
supply chain is unrealistic. There may actually be multiple points where buffering takes place.
Good examples of where the models described in this chapter are used include retail stores,
grocery stores, wholesale distributors, hospital suppliers, and suppliers of repair parts needed
to fix or maintain equipment quickly. Situations in which it is necessary to have the item “instock” are ideal candidates for the models described in this chapter. A distinction that needs to
be made with the models included in this chapter is whether this is a one-time purchase—for
example, for a seasonal item or for use at a special event—or whether the item will be stocked
on an ongoing basis.
Exhibit 20.1 depicts different types of supply chain inventories that would exist in a maketo-stock environment, typical of items directed at the consumer. In the upper echelons of the
supply chain, which are supply points closer to the customer, stock usually is kept so that an
item can be delivered quickly when a customer need occurs. Of course, there are many exceptions, but in general this is the case. The raw materials and manufacturing plant inventory
held in the lower echelon potentially can be managed in a special way to take advantage of
the planning and synchronization that are needed to efficiently operate this part of the supply chain. In this case, the models in this chapter are most appropriate for the upper echelon
inventories (retail and warehouse), and the lower echelon should use the material requirements planning (MRP) technique that will be described in Chapter 21. The applicability of
these models could be different for other environments, such as when we produce directly to
customer order as in the case of an aircraft manufacturer.
The techniques described here are most appropriate when demand is difficult to predict
with great precision. In these models, we characterize demand by using a probability distribution and maintain stock so that the risk associated with stockout is managed. For these applications, the following three models are discussed:
1.
2.
The single-period model. This is used when we are making a one-time purchase of
an item. An example might be purchasing T-shirts to sell at a one-time sporting event.
Fixed–order quantity model. This is used when we want to maintain an item “instock,” and when we resupply the item, a certain number of units must be ordered
each time. Inventory for the item is monitored until it gets down to a level where the
risk of stocking out is great enough that we are compelled to order.
ex hibit 20.1
Supply Chain Inventories—Make-to-Stock Environment
Supply Chain Inventory
Best Model for Managing
Inventory
Retail Store
Inventory
Warehouse
Inventory
Manufacturing
Plant Inventory
Raw Materials
Single-Period, Fixed–Order
Quantity, Fixed–Time Period
(Chapter 20 models)
Material Requirements
Planning
(Chapter 21 model)
517
KEY IDEA
A decoupling point
is where inventory is
carried and allows the
“upstream” part of the
supply chain to operate
relatively independent
of the “downstream”
part.
518
Supply and Demand Planning and Control
Section 4
3.
Inventory (Goldratt’s
definition)
All the money that the
system has invested
in purchasing things it
intends to sell (Goldratt’s
definition).
Fixed–time period model. This is similar to the fixed–order quantity model, and
is used when the item should be in-stock and ready to use. In this case, rather than
monitoring the inventory level and ordering when the level gets down to a critical
quantity, the item is ordered at certain intervals of time, for example, every Friday
morning. This is often convenient when a group of items is ordered together. An
example is the delivery of different types of bread to a grocery store. The bakery
supplier may have 10 or more products stocked in a store, and rather than delivering
each product individually at different times, it is much more efficient to deliver all 10
together at the same time and on the same schedule.
In this chapter, we want to show not only the mathematics associated with great inventory
control but also the “art” of managing inventory. Ensuring accuracy in inventory records is
essential to running an efficient inventory control process. Techniques such as ABC analysis
and cycle counting are essential to the actual management of the system because they focus
attention on the high-value items and ensure the quality of the transactions that affect the
tracking of inventory levels.
Inventory is the stock of any item or resource used in an organization. An inventory system is the set of policies and controls that monitor levels of inventory and determine what levels should be maintained, when stock should be replenished, and how large orders should be.
By convention, manufacturing inventory generally refers to items that contribute to or
become part of a firm’s product output. Manufacturing inventory is typically classified into
raw materials, finished products, component parts, supplies, and work-in-process. In distribution, inventory is classified as in-transit, meaning that it is being moved in the system, and
warehouse, which is inventory in a warehouse or distribution center. Retail sites carry inventory for immediate sale to customers. In services, inventory generally refers to the tangible
goods to be sold and the supplies necessary to administer the service.
The basic purpose of inventory analysis, whether in manufacturing, distribution, retail, or
services, is to specify (1) when items should be ordered and (2) how large the order should
be. Many firms are tending to enter into longer-term relationships with vendors to supply
their needs for perhaps the entire year. This changes the “when” and “how many to order” to
“when” and “how many to deliver.”
Pur pos es o f In ven t o ry
KEY IDEA
Every individual item
in inventory should
be there for a specific
purpose. Also, when
you see an item in
inventory, put a dollar
sign on it. Inventory
is like piles of money
sitting in a warehouse.
All firms (including JIT operations) keep a supply of inventory for the following reasons:
1.
To maintain independence of operations. A supply of materials at a work center
allows that center flexibility in operations. For example, because there are costs for
making each new production setup, this inventory allows management to reduce the
number of setups.
Independence of workstations is desirable on assembly lines as well. The time
it takes to do identical operations will naturally vary from one unit to the next. Therefore, it is desirable to have a cushion of several parts within the workstation so that
shorter performance times can compensate for longer performance times. This way,
the average output can be fairly stable.
2. To meet variation in product demand. If the demand for the product is known precisely, it may be possible (though not necessarily economical) to produce the product
to exactly meet the demand. Usually, however, demand is not completely known, and
a safety or buffer stock must be maintained to absorb variation.
3. To allow flexibility in production scheduling. A stock of inventory relieves the
pressure on the production system to get the goods out. This causes longer lead
times, which permit production planning for smoother flow and lower-cost operation
through larger lot-size production. High setup costs, for example, favor producing a
larger number of units once the setup has been made.
4. To provide a safeguard for variation in raw material delivery time. When material is ordered from a vendor, delays can occur for a variety of reasons: a normal
Inventory Management
Chapter 20
519
Elevated view of a large
distribution warehouse
© Alistair Berg/Getty Images RF
variation in shipping time, a shortage of material at the vendor’s plant causing backlogs, an unexpected strike at the vendor’s plant or at one of the shipping companies, a
lost order, or a shipment of incorrect or defective material.
5. To take advantage of economic purchase order size. There are costs to place
an order: labor, phone calls, typing, postage, and so on. Therefore, the larger each
order is, the fewer the orders that need be written. Also, shipping costs favor larger
orders—the larger the shipment, the lower the per-unit cost.
6. Many other domain-specific reasons. Depending on the situation, inventory may
need to be carried. For example, in-transit inventory is material being moved from
the suppliers to customers and depends on the order quantity and the transit lead
time. Another example is inventory that is bought in anticipation of price changes
such as fuel for jet planes or semiconductors for computers. There are many other
examples.
For each of the preceding reasons (especially for items 3, 4, and 5), be aware that inventory
is costly and large amounts are generally undesirable. Long cycle times are caused by large
amounts of inventory, which are undesirable as well.
I n ve n t or y Cos ts
In making any decision that affects inventory size, the following costs must be considered:
1.
Holding (or carrying) costs. This broad category includes the costs for storage
facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes,
and the opportunity cost of capital. Obviously, high holding costs tend to favor low
inventory levels and frequent replenishment.
2. Setup (or production change) costs. To make each different product involves
obtaining the necessary materials, arranging specific equipment setups, filling out the
required papers, appropriately charging time and materials, and moving out the previous stock of material.
If there were no costs or loss of time in changing from one product to another,
many small lots would be produced. This would reduce inventory levels, with a
resulting savings in cost. One challenge today is to try to reduce these setup costs to
permit smaller lot sizes. (This is the goal of a JIT system.)
520
Supply and Demand Planning and Control
Section 4
3.
4.
Ordering costs. These costs refer to the managerial and clerical costs to prepare the
purchase or production order. Ordering costs include all the details, such as counting
items and calculating order quantities. The costs associated with maintaining the system needed to track orders are also included in ordering costs.
Shortage costs. When the stock of an item is depleted, an order for that item must
either wait until the stock is replenished or be canceled. When the demand is not met
and the order is canceled, this is referred to as a stock out. A backorder is when the
order is held and filled at a later date when the inventory for the item is replenished.
There is a trade-off between carrying stock to satisfy demand and the costs resulting
from stock outs and backorders. This balance is sometimes difficult to obtain because
it may not be possible to estimate lost profits, the effects of lost customers, or lateness penalties. Frequently, the assumed shortage cost is little more than a guess,
although it is usually possible to specify a range of such costs.
Establishing the correct quantity to order from vendors or the size of lots submitted to
the firm’s productive facilities involves a search for the minimum total cost resulting from
the combined effects of four individual costs: holding costs, setup costs, ordering costs, and
shortage costs. Of course, the timing of these orders is a critical factor that may impact inventory cost.
Inde pe nde n t versu s Dep en d en t Deman d
In inventory management, it is important to understand the trade-offs involved in using different types of inventory control logic. Exhibit 20.2 is a framework that shows how characteristics of demand, transaction cost, and the risk of obsolete inventory map into different types of
systems. The systems in the upper left of the exhibit are described in this chapter, and those in
the lower right in Chapter 21.
Transaction cost is dependent on the level of integration and automation incorporated
in the system. Manual systems such as simple two-bin logic depend on human posting of
the transactions to replenish inventory, which is relatively expensive compared to using a
computer to automatically detect when an item needs to be ordered. Integration relates to
how connected systems are. For example, it is common for orders for material to be automatically transferred to suppliers electronically and for these orders to be automatically
captured by the supplier inventory control system. This type of integration greatly reduces
transaction cost.
exhibit 20.2
Inventory-Control-System Design Matrix: Framework Describing
Inventory Control Logic
High
Independent
Manual
two-bin
Reorder point/equal
order period
Demand
Obsolete
inventory
(risk)
Material
requirements
planning
Dependent
High
Transaction costs
Rate-based
synchronous
planning
Low
Low
Inventory Management
Chapter 20
The risk of obsolescence is also an important consideration. If an item is used infrequently
or only for a very specific purpose, there is considerable risk in using inventory control logic
that does not track the specific source of demand for the item. Further, items that are sensitive
to technical obsolescence, such as computer memory chips and processors, need to be managed carefully based on actual need to reduce the risk of getting stuck with inventory that is
outdated.
An important characteristic of demand relates to whether demand is derived from an end
item or is related to the item itself. We use the terms independent demand and d
­ ependent
demand to describe this characteristic. Briefly, the distinction between independent and
dependent demand is this: In independent demand, the demands for various items are unrelated to each other. For example, a workstation may produce many parts that are unrelated
but that meet some external demand requirement. In dependent demand, the need for any one
item is a direct result of the need for some other item, usually a higher-level item of which
it is part.
In concept, dependent demand is a relatively straightforward computational problem.
Required quantities of a dependent-demand item are simply computed, based on the number
needed in each higher-level item in which it is used. For example, if an automobile company
plans on producing 500 cars per day, then obviously it will need 2,000 wheels and tires (plus
spares). The number of wheels and tires needed is dependent on the production levels and
is not derived separately. The demand for cars, on the other hand, is independent—it comes
from many sources external to the automobile firm and is not a part of other products; it is
unrelated to the demand for other products.
To determine the quantities of independent items that must be produced, firms usually turn
to their sales and market research departments. They use a variety of techniques, including
customer surveys, forecasting techniques, and economic and sociological trends, as we discussed in Chapter 18 on forecasting. Because independent demand is uncertain, extra units
must be carried in inventory. This chapter presents models to determine how many units need
to be ordered, and how many extra units should be carried to reduce the risk of stocking out.
521
Independent demand
The demands for these
items are unrelated to
each other, or to activities
that can be predicted with
certainty.
Dependent demand
The need for an item is a
direct result of the need for
some other item, usually
an item of which it is a part.
Also, when the demand for
the item can be predicted
with accuracy due to
a schedule or specific
activitity.
INVENTORY CONT RO L SYSTEMS
An inventory system provides the organizational structure and the operating policies for
maintaining and controlling goods to be stocked. The system is responsible for ordering and
receipt of goods: timing the order placement and keeping track of what has been ordered, how
much, and from whom. The system also must follow up to answer such questions as: Has the
supplier received the order? Has it been shipped? Are the dates correct? Are the procedures
established for reordering or returning undesirable merchandise?
This section divides systems into single-period systems and multiple-period systems. The
classification is based on whether the decision is just a one-time purchasing decision where
the purchase is designed to cover a fixed period of time and the item will not be reordered, or
the decision involves an item that will be purchased periodically where inventory should be
kept in stock to be used on demand. We begin with a look at the one-time purchasing decision
and the single-period inventory model.
LO 20–2
Analyze how different
inventory control systems
work.
A S in g le - Pe r iod Inve ntory Mo del
Certainly, an easy example to think about is the classic single-period (newsperson) problem.
For example, consider the problem that the newsperson has in deciding how many newspapers
to put in the sales stand outside a hotel lobby each morning. If the person does not put enough
papers in the stand, some customers will not be able to purchase a paper and the newsperson
will lose the profit associated with these sales. On the other hand, if too many papers are
placed in the stand, the newsperson will have paid for papers that were not sold during the day,
lowering profit for the day.
Single-period problem
Answers the question of
how much to order when
an item is purchased only
one time and it is expected
that it will be used and
then not reordered.
522
Section 4
Supply and Demand Planning and Control
Actually, this is a very common type
of problem. Consider the person selling
T-shirts promoting a championship basketball or football game. This is especially
difficult, because the person must wait
to learn what teams will be playing. The
shirts can then be printed with the proper
team logos. Of course, the person must
estimate how many people will actually
want the shirts. The shirts sold prior to the
game can probably be sold at a premium
price, whereas those sold after the game
will need to be steeply discounted.
A simple way to think about this is
to consider how much risk we are willing to take for running out of inventory.
Let’s consider that the newsperson selling papers in the sales stand had collected
data over a few months and had found
that, on average, each Monday 90 papers
were sold with a standard deviation of 10
Salesperson Alberto Tilghman, left, displays Philadelphia Phillies
papers (assume that during this time the
merchandise at a Modell’s sporting goods store in Philadelphia.
papers were purposefully overstocked in
© Matt Rourke/AP Images
order not to run out, so they would know
what “real” demand was). With these data,
our newsperson could simply state a service rate that is felt to be acceptable. For example,
the newsperson might want to be 80 percent sure of not running out of papers each Monday.
Recall from your study of statistics, assuming that the probability distribution associated
with the sales of the paper is normal, that if we stocked exactly 90 papers each Monday morning, the risk of stocking out would be 50 percent, because 50 percent of the time we expect
demand to be less than 90 papers and 50 percent of the time we expect demand to be greater
than 90. To be 80 percent sure of not stocking out, we need to carry a few more papers. From
the cumulative standard normal distribution table given in Appendix G, we see that we need
approximately 0.85 standard deviation of extra papers to be 80 percent sure of not stocking
out. A quick way to find the exact number of standard deviations needed for a given probability of stocking out is with the NORMSINV(probability) function in Microsoft Excel (NORMSINV(0.8) = 0.84162). Given our result from Excel, which is more accurate than what we can
get from the tables, the number of extra papers would be 0.84162 × 10 = 8.416, or 9 papers
(There is no way to stock 0.4 paper!).
To make this more useful, it would be good to actually consider the potential profit and
loss associated with stocking either too many or too few papers on the stand. Let’s say that
our newspaper person pays $0.20 for each paper and sells the papers for $0.50. In this case,
the marginal cost associated with underestimating demand is $0.30, the lost profit. Similarly,
the marginal cost of overestimating demand is $0.20, the cost of buying too many papers. The
optimal stocking level, using marginal analysis, occurs at the point where the expected benefits derived from carrying the next unit are less than the expected costs for that unit. Keep in
mind that the specific benefits and costs depend on the problem.
In symbolic terms, define
​ o​​= Cost per unit of demand overestimated
C
​    ​ ​
​Cu​​= Cost per unit of demand underestimated
By introducing probabilities, the expected marginal cost equation becomes
​P​(​C​o​)​≤ ​(​1 − P​)​C​u​
Inventory Management
Chapter 20
where P is the probability that the unit will not be sold and 1 – P is the probability of it being
sold because one or the other must occur. (The unit is sold or is not sold.)1
Then, solving for P, we obtain
​C​u​
​P ≤ _____
​
​
​C​o​+ ​C​u​
[20.1]
This equation states that we should continue to increase the size of the order so long as the
probability of selling what we order is equal to or less than the ratio Cu/(Co + Cu).
Returning to our newspaper problem, our cost of overestimating demand (Co) is $0.20
per paper and the cost of underestimating demand (Cu) is $0.30. The probability therefore
is 0.3/(0.2 + 0.3) = 0.6. Now we need to find the point on our demand distribution that corresponds to the cumulative probability of 0.6. Using the NORMSINV function to get the
number of standard deviations (commonly referred to as the Z-score) of extra newspapers
to carry, we get 0.253, which means we should stock 0.253(10) = 2.53 or 3 extra papers.
The total number of papers for the stand each Monday morning, therefore, should be
93 papers.
Single-period inventory models are useful for a wide variety of service and manufacturing
applications. Consider the following:
1.
2.
3.
Overbooking of airline flights. It is common for customers to cancel flight reservations for a variety of reasons. Here, the cost of underestimating the number of cancellations is the revenue lost due to an empty seat on a flight. The cost of overestimating
cancellations is the awards, such as free flights or cash payments, that are given to
customers unable to board the flight.
Ordering of fashion items. A problem for a retailer selling fashion items is that
often only a single order can be placed for the entire season. This is often caused by
long lead times and the limited life of the merchandise. The cost of underestimating
demand is the lost profit due to sales not made. The cost of overestimating demand is
the cost that results when it is discounted.
Any type of one-time order. For example, ordering T-shirts for a sporting event or
printing maps that become obsolete after a certain period of time.
EXAMPLE 20.1: Hotel Reservations
A hotel near the university always fills up on the evening before football games. History has
shown that when the hotel is fully booked, the number of last-minute cancellations has a mean
of 5 and a standard deviation of 3. The average room rate is $80. When the hotel is overbooked, the policy is to find a room in a nearby hotel and to pay for the room for the customer.
This usually costs the hotel approximately $200 because rooms booked on such late notice are
expensive. How many rooms should the hotel overbook?
SOLUTION
The cost of underestimating the number of cancellations is $80 and the cost of overestimating
cancellations is $200.
​C​u​
$80
​P ≤ _____
​
​= __________
​
​ = 0.2857​
​C​o​+ ​C​u​ $200 + $80
Using NORMSINV(.2857) from Excel gives a Z-score of –0.56599. The negative value indicates that we should overbook by a value less than the average of 5. The actual value should
be –0.56599(3) = –1.69797, or 2 reservations less than 5. The hotel should overbook three
reservations on the evening prior to a football game.
523
524
Supply and Demand Planning and Control
Section 4
Another common method for analyzing this type of problem is with a discrete probability distribution found using actual data and marginal analysis. For our hotel, consider that we have
collected data and our distribution of no-shows is as follows.
Number of
No-Shows
Probability
Cumulative
Probability
0
0.05
0.05
1
0.08
0.13
2
0.10
0.23
3
0.15
0.38
4
0.20
0.58
5
0.15
0.73
6
0.11
0.84
7
0.06
0.90
8
0.05
0.95
9
0.04
0.99
10
0.01
1.00
Using these data, we can create a table showing the impact of overbooking. Total expected
cost of each overbooking option is then calculated by multiplying each possible outcome by
its probability and summing the weighted costs. The best overbooking strategy is the one with
minimum cost.
Number of Reservations Overbooked
NoShows Probability
Fixed–order quantity
model (Q-model)
An inventory control
model where the amount
requisitioned is fixed
and the actual ordering
is triggered by inventory
dropping to a specified
level of inventory.
Fixed–time period
model (P-model)
An inventory control model
that specifies inventory
is ordered at the end of
a predetermined time
period. The interval of time
between orders is fixed
and the order quantity
varies.
3
4
0
0.05
0
200 400
600
800 1,000 1,200 1,400 1,600 1,800 2,000
1
0.08
80
0 200
400
600
800 1,000 1,200 1,400 1,600 1,800
2
0.1
160
80
0
200
400
600
800 1,000 1,200 1,400 1,600
3
0.15
240
160
80
0
200
400
600
800 1,000 1,200 1,400
4
0.2
320
240 160
80
0
200
400
600
800 1,000 1,200
5
0.15
400
320 240
160
80
0
200
400
600
800 1,000
6
0.11
480
400 320
240
160
80
0
200
400
600
800
7
0.06
560
480 400
320
240
160
80
0
200
400
600
8
0.05
640
560 480
400
320
240
160
80
0
200
400
9
0.04
720
640 560
480
400
320
240
160
80
0
200
10
0.01
800
720 640
560
480
400
320
240
160
80
0
Expected cost
0
1
2
5
6
7
8
9
10
337.6 271.6 228 212.4 238.8 321.2 445.6 600.8 772.8 958.8 1,156
From the table, the minimum total cost is when three extra reservations are taken. This
approach, using discrete probability, is useful when valid historic data are available.
M ultipe r io d In ven t o ry Syst ems
There are two general types of multiperiod inventory systems: fixed–order quantity models
(also called the economic order quantity, EOQ, and Q-model) and fixed–time period models
(also referred to variously as the periodic system, periodic review system, fixed–order interval system, and P-model). Multiperiod inventory systems are designed to ensure that an item
will be available on an ongoing basis throughout the year. Usually, the item will be ordered
multiple times throughout the year where the logic in the system dictates the actual quantity
ordered and the timing of the order.
The basic distinction is that fixed–order quantity models are “event triggered” and fixed–
time period models are “time triggered.” That is, a fixed–order quantity model initiates an
order when the event of reaching a specified reorder level occurs. This event may take place
at any time, depending on the demand for the items considered. In contrast, the fixed–time
Inventory Management
Chapter 20
period model is limited to placing orders at the end of a predetermined time period; only the
passage of time triggers the model.
To use the fixed–order quantity model (which places an order when the remaining inventory drops to a predetermined order point, R), the inventory remaining must be continually
monitored. Thus, the fixed–order quantity model is a perpetual system, which requires that
every time a withdrawal from inventory or an addition to inventory is made, records must be
updated to reflect whether the reorder point has been reached. In a fixed–time period model,
counting takes place only at the review period. (We will discuss some variations of systems
that combine features of both.)
Some additional differences tend to influence the choice of systems (also see Exhibit 20.3):
∙
∙
∙
∙
The fixed–time period model has a larger average inventory because it must also protect against stockout during the review period, T; the fixed–order quantity model has no
review period.
The fixed–order quantity model favors more expensive items because average inventory is lower.
The fixed–order quantity model is more appropriate for important items such as critical
repair parts because there is closer monitoring and therefore quicker response to potential stockout.
The fixed–order quantity model requires more time to maintain because every addition
or withdrawal is logged.
Exhibit 20.4 shows what occurs when each of the two models is put into use and becomes
an operating system. As we can see, the fixed–order quantity system focuses on order quantities and reorder points. Procedurally, each time a unit is taken out of stock, the withdrawal is
logged and the amount remaining in inventory is immediately compared to the reorder point.
If it has dropped to this point, an order for Q items is placed. If it has not, the system remains
in an idle state until the next withdrawal.
In the fixed–time period system, a decision to place an order is made after the stock has
been counted or reviewed. Whether an order is actually placed depends on the inventory position at that time.
Fi xe d – Or de r Qua ntity M o de ls
Fixed–order quantity models attempt to determine the specific point, R, at which an order will
be placed and the size of that order, Q. The order point, R, is always a specified number of
units. An order of size Q is placed when the inventory available (currently in stock and on
ex hibit 20.3
Fixed–Order Quantity and Fixed–Time Period Differences
Q-Model
P-Model
Feature
Fixed–Order Quantity Model
Fixed–Time Period Model
Order quantity
Q—constant (the same amount
ordered each time)
q—variable (varies each time
order is placed)
When to place order
R—when the inventory position
drops to the reorder level
T—when the review period
arrives
Recordkeeping
Each time a withdrawal or addition is made
Counted only at review period
Size of inventory
Less than fixed–time period
model
Larger than fixed–order quantity
model
Time to maintain
Higher due to perpetual
recordkeeping
Efficient, because multiple items
can be ordered at the same time
Type of items
Higher-priced, critical, or important items
Typically used with lower-cost
items
525
526
Supply and Demand Planning and Control
Section 4
exhibit 20.4
Comparison of Fixed–Order Quantity and Fixed–Time Period
Reordering Inventory Systems
Q-Model
Fixed–Order
Quantity System
P-Model
Fixed–Time Period
Reordering System
Idle state
Waiting for demand
Idle state
Waiting for demand
Demand occurs
Unit withdrawn
from inventory or
backordered
Demand occurs
Units withdrawn from
inventory or backordered
Compute inventory position
Position = On-hand +
On-order – Backorder
No
Is position ≤
Reorder point?
Yes
Issue an order for
exactly Q units
No
Has review
time
arrived?
Yes
Compute inventory position
Position = On-hand +
On-order – Backorder
Compute order quantity to
bring inventory up to
required level
Issue an order for the
number of units needed
Inventory position
The amount on hand
plus on-order minus
backordered quantities. In
the case where inventory
has been allocated for
special purposes, the
inventory position is
reduced by these allocated
amounts.
order) reaches the point R. Inventory position is defined as the on-hand plus on-order minus
backordered quantities. The solution to a fixed–order quantity model may stipulate something
like this: When the inventory position drops to 36, place an order for 57 more units.
The simplest models in this category occur when all aspects of the situation are known
with certainty. If the annual demand for a product is 1,000 units, it is precisely 1,000—not
1,000 plus or minus 10 percent. The same is true for setup costs and holding costs. Although
the assumption of complete certainty is rarely valid, it provides a good basis for our coverage
of inventory models.
Exhibit 20.5 and the discussion about deriving the optimal order quantity are based on the
following characteristics of the model. These assumptions are unrealistic, but they represent a
starting point and allow us to use a simple example.
∙
∙
∙
∙
∙
∙
Demand for the product is constant and uniform throughout the period.
Lead time (time from ordering to receipt) is constant.
Price per unit of product is constant.
Inventory holding cost is based on average inventory.
Ordering or setup costs are constant.
All demands for the product will be satisfied. (No backorders are allowed.)
The “sawtooth effect” relating Q and R in Exhibit 20.5 shows that when the inventory position drops to point R, a reorder is placed. This order is received at the end of time period L,
which does not vary in this model.
Inventory Management
ex hibit 20.5
Chapter 20
527
Basic Fixed–Order Quantity Model
Q-Model
Inventory
on
Q
hand
R
Q
Q
L
L
Time
Q
L
In constructing any inventory model, the first step is to develop a functional relationship
between the variables of interest and the measure of effectiveness. In this case, because we are
concerned with cost, the following equation becomes:
Annual
Annual
Annual
​​     Total​ ​ = ​
​ ​+ ​
​ ​+ ​
​ ​​
annual cost purchase cost ordering cost holding cost
or
where
Q
​TC = DC + __
​D ​S + __
​ ​H​​
Q
2
[20.2]
TC = Total annual cost
D = Demand (annual)
C = Cost per unit
Q = Quantity to be ordered (the optimal amount is termed the economic order quantity—
EOQ—or Qopt)
S = Setup cost or cost of placing an order
R = Reorder point
L = Lead time
H = Annual holding and storage cost per unit of average inventory (often, holding cost is
taken as a percentage of the cost of the item, such as H = iC, where i is the percent
carrying cost)
On the right side of the equation, DC is the annual purchase cost for the units, (D/Q)S is the
annual ordering cost (the actual number of orders placed, D/Q, times the cost of each order,
S), and (Q/2)H is the annual holding cost (the average inventory, Q/2, times the cost per unit
for holding and storage, H). These cost relationships are graphed in Exhibit 20.6.
The second step in model development is to find that optimal order quantity Qopt at which
total cost is a minimum. In Exhibit 20.6, the total cost is minimal at the point where the slope
of the curve is zero. Using calculus, we take the derivative of total cost with respect to Q and
set this equal to zero. For the basic model considered here, the calculations are
Q
TC = DC + __
​D ​S + __
​ ​H
​
Q
2
​
​ ​ ​
⎛ − DS ⎞ __
____
​dTC ​= 0 + ​ ​_
​
​ ​+ ​H ​= 0 ​
⎝ ​Q​2​ ⎠ 2
dQ
⎜
____
​Q​opt​= ​ ____
​2DS ​
H
√
⎟
[20.3]
Optimal order quantity
(Qopt)
This order size minimizes
total annual cost.
528
Section 4
Supply and Demand Planning and Control
Annual Product Costs, Based on Size of the Order
exhibit 20.6
TC (total cost)
Q
2 H (holding cost)
DC (annual cost of items)
D
Q S (ordering cost)
Cost
Qopt
Order quantity size (Q)
Reorder point (R)
An order is placed when
inventory drops to this
level.
Because this simple model assumes constant demand and lead time, neither safety stock nor
stockout cost is necessary, and the reorder point, R, is simply
​​R = d ​
​  ¯L​​
[20.4]
where
¯​= Average daily demand (constant)
​​ d ​
L = Lead time in days (constant)
EXAMPLE 20.2: Economic Order Quantity and Reorder Point
Find the economic order quantity and the reorder point, given
Annual demand ​(​D​)​ = 1, 000 units
Average daily demand ​(d​¯​)​ = 1, 000 ∕365
Ordering cost ​(​S​)​ = $5 per order
​
​ ​
​
​​ ​
​
Holding cost (​ ​H)​ ​ = $1.25 per unit per year
Lead time (​ ​L)​ ​ = 5 days
Cost per unit ​(​C​)​ = $12.50
What quantity should be ordered?
SOLUTION
The optimal order quantity is
____
________
_____
2(1, 000 ) 5
​√ 2DS ​
​Q​opt​= ____
​
​= ​ ________
​
​ = ​√ 8, 000 ​= 89.4 units​
H
The reorder point is
√
1.25
1, 000
​R = d ​
​  ¯L = _____
​
​(5 ) = 13.7 units​
365
Rounding to the nearest unit, the inventory policy is as follows: When the inventory
­position drops to 14, place an order for 89 more.
The total annual cost will be
Q
TC = DC + __
​D ​S + __
​ ​H
Q
2
⎛
⎞ 1,
​
​
​
​ 000
​
​ ​= 1, 000​ ​12.50​ ​+ _
​
​(​5​)​+ _
​89 ​(​1.25​)​
⎝
⎠
89
2
​ = $12, 611.80
⎜
⎟
Inventory Management
Chapter 20
529
Note that the total ordering cost (1,000/89) × 5 = $56.18 and the total carrying cost (89/2) ×
1.25 = $55.625 are very close but not exactly the same due to rounding Q to 89.
Note that, in this example, the purchase cost of the units was not required to determine
the order quantity and the reorder point because the cost was constant and unrelated to
order size.
E s t a b l i s h i n g S a f e t y S t o c k L e v e l s The previous model assumed that demand
was constant and known. In the majority of cases, though, demand is not constant but varies
from day to day. Safety stock must therefore be maintained to provide some level of protection
against stock outs. Safety stock can be defined as the amount of inventory carried in addition
to the expected demand. In a normal distribution, this would be the mean. For example, if our
average monthly demand is 100 units and we expect next month to be the same, if we carry
120 units, then we have 20 units of safety stock.
Safety stock can be determined based on many different criteria. A common approach is
for a company to simply state that a certain number of weeks of supply needs to be kept in
safety stock. It is better, though, to use an approach that captures the variability in demand.
For example, an objective may be something like “set the safety stock level so that there
will only be a 5 percent chance of stocking out if demand exceeds 300 units.” We call this
approach to setting safety stock the probability approach.
T h e P r o b a b i l i t y A p p r o a c h Using the probability criterion to determine safety
stock is pretty simple. With the models described in this chapter, we assume that the demand
over a period of time is normally distributed with a mean and a standard deviation. Again,
remember that this approach considers only the probability of running out of stock, not how
many units we are short. To determine the probability of stocking out over the time period, we
can simply plot a normal distribution for the expected demand and note where the amount we
have on hand lies on the curve.
Let’s take a few simple examples to illustrate this. Say we expect demand to be 100 units
over the next month, and we know that the standard deviation is 20 units. If we go into the
month with just 100 units, we know that our probability of stocking out is 50 percent. Half
of the months we would expect demand to be greater than 100 units; half of the months we
would expect it to be less than 100 units. Taking this further, if we ordered a month’s worth
of inventory of 100 units at a time and received it at the beginning of the month, over the long
run we would expect to run out of inventory in six months of the year.
If running out this often was not acceptable, we would want to carry extra inventory to
reduce this risk of stocking out. One idea might be to carry an extra 20 units of inventory
for the item. In this case, we would still order a month’s worth of inventory at a time, but we
would schedule delivery to arrive when we still have 20 units remaining in inventory. This
would give us that little cushion of safety stock to reduce the probability of stocking out. If
the standard deviation associated with our demand was 20 units, we would then be carrying
one standard deviation worth of safety stock. Looking at the cumulative standard normal distribution (Appendix G), and moving one standard deviation to the right of the mean, gives a
probability of 0.8413. So approximately 84 percent of the time we would not expect to stock
out, and 16 percent of the time we would. Now, if we order every month, we would expect to
stock out approximately two months per year (0.16 × 12 = 1.92). For those using Excel, given
a z value, the probability can be obtained with the NORMSDIST function.
It is common for companies using this approach to set the probability of not stocking out
at 95 percent. This means we would carry about 1.64 standard deviations of safety stock,
or 33 units (1.64 × 20 = 32.8) for our example. Once again, keep in mind that this does not
mean that we would order 33 units extra each month. Rather, it means that we would still
order a month’s worth each time, but we would schedule the receipt so that we could expect
to have 33 units in inventory when the order arrives. In this case, we would expect to stock
out approximately 0.6 month per year, or that stockouts would occur in 1 of every 20 months.
Safety stock
The amount of inventory
carried in addition to the
expected demand.
530
Section 4
Supply and Demand Planning and Control
F i x e d – O r d e r Q u a n t i t y M o d e l w i t h S a f e t y S t o c k A fixed–order quantity
system perpetually monitors the inventory level and places a new order when stock reaches
some level, R. The danger of stockout in this model occurs only during the lead time, between
the time an order is placed and the time it is received. As shown in Exhibit 20.7, an order is
placed when the inventory position drops to the reorder point, R. During this lead time, L, a
range of demands is possible. This range is determined either from an analysis of past demand
data or from an estimate (if past data are not available).
The amount of safety stock depends on the service level desired, as previously discussed.
The quantity to be ordered, Q, is calculated in the usual way considering the demand, shortage cost, ordering cost, holding cost, and so forth. A fixed–order quantity model can be used
to compute Q, such as the simple Qopt model previously discussed. The reorder point is then
set to cover the expected demand during the lead time plus a safety stock determined by the
desired service level. Thus, the key difference between a fixed–order quantity model where
demand is known and one where demand is uncertain is in computing the reorder point. The
order quantity is the same in both cases. The uncertainty element is taken into account in the
safety stock.
The reorder point is
​  ¯L + z ​σ​L​​​
​​R = d ​
[20.5]
​​where
R = Reorder point in units
​​  ¯​= Average daily demand
d ​
L = Lead time in days (time between placing an order and receiving the items)
z = Number of standard deviations for a specified service probability
σL = Standard deviation of usage during lead time
The term zσL is the amount of safety stock. Note that if safety stock is positive, the effect
is to place a reorder sooner. That is, R without safety stock is simply the average demand during the lead time. If lead time usage was expected to be 20, for example, and safety stock was
computed to be 5 units, then the order would be placed sooner, when 25 units remained. The
greater the safety stock, the sooner the order is placed.
C o m p u t i n g d , σ L , a n d z Demand during the replenishment lead time is really an
estimate or forecast of expected use of inventory from the time an order is placed to when it
is received. It may be a single number (for example, if the lead time is a month, the demand
may be taken as the previous year’s demand divided by 12), or it may be a summation of
expected demands over the lead time (such as the sum of daily demands over a 30-day lead
time). For the daily demand situation, d can be a forecast demand using any of the models
exhibit 20.7
Fixed–Order Quantity Model
Q-Model
Number
of units
on hand
Q
R
Range of demand
Safety stock
0
Time
L
Stockout
Inventory Management
Chapter 20
in Chapter 18 on forecasting. For example, if a 30-day period was used to calculate d, then a
simple average would be
​∑ n ​​d​i​
​d¯​= ______
​ i=1
n ​
​
​
30
​∑ i=1​​d​i​
______
​=​​
​
30
[20.6]
where n is the number of days.
The standard deviation of the daily demand is
___________
​ ​∑ ni=1​(​​d​i​− d​¯​)​2​
√
​σ​d​= __________
​
​
n
___________
​
​​​
​ ​∑ 30
​(​​d​i​− d​¯)​ ​2​
√
i=1
​=​​__________​
30
[20.7]
Because σd refers to one day, if lead time extends over several days, we can use the statistical premise that the standard deviation of a series of independent occurrences is equal to the
square root of the sum of the variances. That is, in general,
____________
​σL​​= ​√ ​σ
​21​+ ​σ​22​+ . . . +​σ​2L​
[20.8]
​​For example, suppose we computed the standard deviation of demand to be 10 units per day.
If our lead time to get an order is five days, the standard deviation for the five-day period,
assuming each day can be considered independent, is
___________________________
​σ​5​= ​√ ​(
​10​)​2​+ ​(​10​)​2​+ ​(​10​)​2​+ ​(​10​)​2​+ ​(​10​)​2​ = 22.36​
Next we need to find z, the number of standard deviations of safety stock.
Suppose we wanted our probability of not stocking out during the lead time to be 0.95. The
z value associated with a 95 percent probability of not stocking out is 1.64 (see Appendix G or
use the Excel NORMSINV function). Given this, safety stock is calculated as follows:
SS = z ​σ​L​
​​
​ ​​
= 1.64​ ×​ 22.36​ ​​​
​ = 36.67
​
[20.9]
We now compare two examples. The difference between them is that in the first, the variation in demand is stated in terms of standard deviation over the entire lead time, while in the
second, it is stated in terms of standard deviation per day.
EXAMPLE 20.3: Reorder Point
Consider an economic order quantity case where annual demand D = 1,000 units, economic
order quantity Q = 200 units, the desired probability of not stocking out P = .95, the standard
deviation of demand during lead time σL = 25 units, and lead time L = 15 days. Determine the
reorder point. Assume that demand is over a 250-workday year.
SOLUTION
In our example,
1, 000
¯ = _____
​​ d ​
​
​ = 4​, and lead time is 15 days. We use the equation
250
R = d​¯​L + z ​σ​L​
​ ​
​
​ ​
​ ​= 4​(​15​)​+ z​​(​25​)​
531
532
Section 4
Supply and Demand Planning and Control
In this case, z is 1.64.
Completing the solution for R, we have
R = 4(15) + 1.64(25) = 60 + 41 = 101 units
This says that when the stock on hand gets down to 101 units, order 200 more.
EXAMPLE 20.4: Order Quantity and Reorder Point
Daily demand for a certain product is normally distributed, with a mean of 60 and a standard
deviation of 7. The source of supply is reliable and maintains a constant lead time of six days.
The cost of placing the order is $10 and annual holding costs are $0.50 per unit. There are
no stock-out costs, and unfilled orders are filled as soon as the order arrives. Assume sales
occur over the entire 365 days of the year. Find the order quantity and reorder point to satisfy a
95 percent probability of not stocking out during the lead time.
SOLUTION
In this problem we need to calculate the order quantity Q as well as the reorder point R.
​d¯​= 60
S = $10
​σ
​
​
=
7​
​
​ H = $0.50​
​ ​
d
​D = 60​(​365​)​ L = 6
The optimal order quantity is
____
__________
_______
2​​(​60​)​365​​(​10​)​
​Q​opt​= ​ ____
​2DS ​ = ​ __________
​
​ = ​√ 876, 000 ​= 936 units​
√
H
√
0.50
To compute the reorder point, we need to calculate the amount of product used during the
lead time and add this to the safety stock.
The standard deviation of demand during the lead time of six days is calculated from the
variance of the individual days. Because each day’s demand is independent,2
√
____
L
_____
​σ​L​= ​ ​∑​  ​​ ​σ​2d​ ​ = ​√ 6 ​(​7​)​2​ = 17.15​
i=1
Once again, z is 1.64.
​R = d ​
​  ¯L + z ​σ​L​= 60​​(​6​)​+ 1.64​​(​17.15​)​= 388 units​
To summarize the policy derived in this example, an order for 936 units is placed whenever
the number of units remaining in inventory drops to 388.
Fixe d– Time Perio d Mo d els
In a fixed–time period system, inventory is counted only at particular times, such as every
week or every month. Counting inventory and placing orders periodically are desirable in
situations such as when vendors make routine visits to customers and take orders for their
complete line of products, or when buyers want to combine orders to save transportation
costs. Other firms operate on a fixed time period to facilitate planning their inventory count;
for example, Distributor X calls every two weeks and employees know that all Distributor X’s
product must be counted.
Inventory Management
Chapter 20
Fixed–time period models generate order quantities that vary from period to period,
depending on the usage rates. These generally require a higher level of safety stock than a
fixed–order quantity system. The fixed–order quantity system assumes continual tracking of
inventory on hand, with an order immediately placed when the reorder point is reached. In
contrast, the standard fixed–time period models assume that inventory is counted only at the
time specified for review. It is possible that some large demand will draw the stock down to
zero right after an order is placed. This condition could go unnoticed until the next review
period. Then, the new order, when placed, still takes time to arrive. Thus, it is possible to be
out of stock throughout the entire review period, T, and order lead time, L. Safety stock, therefore, must protect against stock outs during the review period itself, as well as during the lead
time from order placement to order receipt.
F i x e d – T i m e P e r i o d M o d e l w i t h S a f e t y S t o c k In a fixed–time period
system, reorders are placed at the time of review (T), and the safety stock that must be
reordered is
​Safety stock = z ​σ​T+L​
[20.10]
​​Exhibit 20.8 shows a fixed–time period system with a review cycle of T and a constant
lead time of L. In this case, demand is randomly distributed about a mean d. The quantity to
order, q, is
Inventory currently
Average demand
Order
Safety
on
hand (plus on​
​
​ ​ =
​
​​ −  ​
​
​​
over the​ ​ ​ + ​
quantity
​​
​  ​  vulnerable period
​
​  stock ​
​
​  ​​​
order, if any)
q
​=       d​¯​(​T + L​)​
+   z ​σ​ ​ −                I
[20.11]
T+L
where
q = Quantity to be ordered
T = The number of days between reviews
L = Lead time in days (time between placing an order and receiving it)
¯​= Forecast average daily demand
​​ d ​
z = Number of standard deviations for a specified service probability
σT + L = Standard deviation of demand over the review and lead time
I = Current inventory level (includes items on order)
ex hibit 20.8
Inventory
on hand
(in units)
Safety
stock
Fixed–Time Period Inventory Model
Place
order
Place
order
P-Model
Place
order
Stockout
L
T
L
T
Time
L
T
Note: The demand, lead time, review period, and so forth can be any time units such as days, weeks, or
years so long as they are consistent throughout the equation.
533
534
Section 4
Supply and Demand Planning and Control
In this model, demand ( ¯
​​ ​d​​​) can be forecast and revised each review period if desired, or the
yearly average may be used if appropriate. We assume that demand is normally distributed.
The value of z is dependent on the probability of stocking out and can be found using
Appendix G or by using the Excel NORMSINV function.
EXAMPLE 20.5: Quantity to Order
Daily demand for a product is 10 units, with a standard deviation of 3 units. The review period
is 30 days, and the lead time is 14 days. Management has set a policy of satisfying 98 percent
of demand from items in stock. At the beginning of this review period, there are 150 units in
inventory.
How many units should be ordered?
SOLUTION
The quantity to order is
q = d ​
​  ¯​(​T + L​)​+ z ​σ​T+L​− I
​ ​​
​
​
​​
​ = 10(30 + 14 ) + z ​σ​T+L​− 150
Before we can complete the solution, we need to find σT1L and z. To find σT1L, we use the
notion, as before, that the standard deviation of a sequence of independent random variables
equals the square root of the sum of the variances. Therefore, the standard deviation during
the period T + L is the square root of the sum of the variances for each day:
√
_____
T+L
​σ​T+L​= ​ ​∑​​σ​2d​
i=1
[20.12]
​​Because each day is independent and σd is constant,
________
___________
​σ​T+L​= ​√ ​(​T + L​)​σ​2d​ = ​√ ​(​30 + 14​)​(​3​)​2​ = 19.90​
The z value for P = 0.98 is 2.05.
The quantity to order, then, is
​q = d ​
​  ¯​(​T + L​)​+ z ​σ​T+L​− I = 10​​(​30 + 14​)​+ 2.05​​(​19.90​)​− 150 = 331 units​
To ensure a 98 percent probability of not stocking out, order 331 units at this review period.
Inve ntor y Tu rn C alcu latio n
Inventory turn
A measure of the expected
number of times inventory
is replaced over a year.
It is important for managers to realize that how they run items using inventory control logic
relates directly to the financial performance of the firm. A key measure that relates to company performance is inventory turn. Recall that inventory turn is calculated as follows:
Cost of goods sold
​Inventory turn = ____________________
​
​​
Average inventory value
So what is the relationship between how we manage an item and the inventory turn for that
item? Here, let us simplify things and consider just the inventory turn for an individual
item or a group of items. First, if we look at the numerator, the cost of goods sold for an
individual item relates directly to the expected yearly demand (D) for the item. Given a
cost per unit (C) for the item, the cost of goods sold is just D times C. Recall this is the
same as what was used in our total cost equation when calculating. Next, consider average
inventory value. Recall from EOQ that the average inventory is Q/2, which is true if we
assume that demand is constant. When we bring uncertainty into the equation, safety stock
is needed to manage the risk created by demand variability. The fixed–order quantity model
Inventory Management
Chapter 20
535
and fixed–time period model both have equations for calculating the safety stock required
for a given probability of stocking out. In both models, we assume that, when going through
an order cycle, half the time we need to use the safety stock and half the time we do not. So,
on average, we expect the safety stock (SS) to be on hand. Given this, the average inventory
is equal to the following:
​Average inventory value = ​(​Q / 2 + SS​)​C​
[20.13]
​​The inventory turn for an individual item then is
DC
​
​= ______
​ D
​
​Inventory turn = _________
(​ ​Q ∕ 2 + SS​)​C Q ∕ 2 + SS
[20.14]
​​
EXAMPLE
20.6: Average Inventory Calculation—Fixed–Order Quantity Model
Suppose the following item is being managed using a fixed–order quantity model with safety stock.
Annual demand (D) = 1,000 units
Order quantity (Q) = 300 units
Safety stock (SS) = 40 units
What are the average inventory level and inventory turn for the item?
SOLUTION
Average inventory = Q / 2 + SS = 300 / 2 + 40 = 190 units
​​
​ ​​
1, 000
Inventory turn = ______
​ D
​= _____
​
​= 5.263 turns per year
Q / 2 + SS
190
EXAMPLE 20.7: Average Inventory Calculation—Fixed–Time Period Model
Consider the following item that is being managed using a fixed–time period model with
safety stock.
Weekly demand (d) = 50 units
Review cycle (T) = 3 weeks
Safety stock (SS) = 30 units
What are the average inventory level and inventory turn for the item?
SOLUTION
Here we need to determine how many units we expect to order each cycle. If we assume that
demand is fairly steady, then we would expect to order the number of units that we expect
demand to be during the review cycle. This expected demand is equal to dT if we assume
there is no trend or seasonality in the demand pattern.
​Average inventory = dT∕ 2 + SS = 50​(​3​)​∕ 2 + 30 = 105 units​
​​
​​​
52​(​50​)​
Inventory turn = _______
​ 52d ​= _____
​
​= 24.8 turns per year
105
dT ∕ 2 + SS
Here we assume the firm operates 52 weeks in the year.
Price-break model
P r i ce - B r e a k M ode l
The price-break model deals with the fact that, generally, the selling price of an item varies with the order size. This is a discrete or step change rather than a per-unit change. For
This model is useful for
finding the order quantity
of an item when the price
of the item varies with the
order size.
536
Supply and Demand Planning and Control
Section 4
example, wood screws may cost $0.02 each for 1 to 99 screws, $1.60 per 100, and $13.50
per 1,000. To determine the optimal quantity of any item to order, we simply solve for
the economic order quantity for each price and at the point of price change. But not all of
the economic order quantities determined by the formula are feasible. In the wood screw
example, the Qopt formula might tell us that the optimal decision at the price of 1.6 cents
is to order 75 screws. This would be impossible, however, because 75 screws would cost
2 cents each.
In general, to find the lowest-cost order quantity, we need to calculate the economic
order quantity for each possible price and check to see whether the quantity is feasible. It
is ­possible that the economic order quantity that is calculated is either higher or lower than
the range to which the price corresponds. Any feasible quantity is a potential candidate
for order quantity. We also need to calculate the cost at each of the price-break quantities,
because we know that price is feasible at these points and the total cost may be lowest at
one of these values.
The calculations can be simplified a little if holding cost is based on a percentage of unit
price (they will be in all the examples and problems given in this book). In this case, we only
need to look at a subset of the price-break quantities. The following two-step procedure can
be used:
Step 1. Sort the prices from lowest to highest and then, beginning with the lowest price,
calculate the economic order quantity for each price level until a feasible economic order
quantity is found. By feasible, we mean that the quantity is in the correct corresponding
range for that price.
Step 2. If the first feasible economic order quantity is for the lowest price, this quantity
is best and you are finished. Otherwise, calculate the total cost for the first feasible economic order quantity (you did these from lowest to highest price) and also calculate the
total cost at each price break lower than the price associated with the first feasible economic order quantity. This is the lowest order quantity at which you can take advantage of
the price break. The optimal Q is the one with the lowest cost.
Looking at Exhibit 20.9, we see that order quantities are solved from right to left, or from
the lowest unit price to the highest, until a valid Q is obtained. Then, the order quantity at each
price break above this Q is used to find which order quantity has the least cost—the computed
Q or the Q at one of the price breaks.
exhibit 20.9
Curves for Three Separate Order Quantity Models in a Three-Price-Break Situation (red line
depicts feasible range of purchases)
1,100
1,000
@ C = $4.50
900
$5.00
@C=
800
Ordering
cost and
holding
cost
700
$3.90
@C=
600
500
400
300
666
200
632
100
100
200
300
400
500
716
600
700
Units
800
900
1,000
1,100
1,200
1,300
Inventory Management
Chapter 20
EXAMPLE 20.8: Price Break
Consider the following case, where
D = 10,000 units (annual demand)
S = $20 to place each order
i = 20 percent of cost (annual carrying cost, storage, interest, obsolescence, etc.)
C = Cost per unit (according to the order size; orders of 0 to 499 units, $5.00 per unit; 500
to 999, $4.50 per unit; 1,000 and up, $3.90 per unit)
What quantity should be ordered?
SOLUTION
The appropriate equations from the basic fixed–order quantity case are
Q
​TC = DC + __
​D ​S + __
​ ​iC​
Q
2
and
____
​Q = ​ ____
​2DS ​
iC
√
[20.15]
​​Solving for the economic order size, we obtain
@ C = $3.90,
Q = 716
Not feasible
@ C = $4.50,
Q = 667
Feasible, cost = $45,600
Check Q = 1,000,
Cost = $39,590
Optimal solution
In Exhibit 20.9, which displays the cost relationship and order quantity range, note that
most of the order quantity–cost relationships lie outside the feasible range and that only a
single, continuous range results. This should be readily apparent because, for example, the
first order quantity specifies buying 632 units at $5.00 per unit. However, if 632 units are
ordered, the price is $4.50, not $5.00. The same holds true for the third order quantity, which
specifies an order of 716 units at $3.90 each. This $3.90 price is not available on orders of less
than 1,000 units.
Exhibit 20.10 itemizes the total costs at the economic order quantities and at the price
breaks. The optimal order quantity is shown to be 1,000 units.
ex hibit 20.10
Relevant Costs in a Three-Price-Break Model
Q = 632
Where
c = $5
Holding and ordering cost
Item cost (DC)
Total cost
Q = 716
Where
c = $3.90
667
___
​
​(0.20)4.50
Holding cost
⎛__
Q ⎞
⎝​ ​2 ​iC⎠​
Ordering cost
⎛__
D ⎞
⎝​ ​Q ​S⎠​
Q = 667
Where
c = $4.50
2
Not feasible
1, 000
​_____​(0.20)3.90
2
= $300.15​
10, 000​(​20​)​
________
​
​
667
= $299.85​
Price
Break
1,000
Not feasible
= $390​
10, 000​(​20​)​
________
​
​
1, 000
= $200​
$600.00
$590
10,000(4.50)
10,000(3.90)
$45,600
$39,590
537
538
Section 4
Supply and Demand Planning and Control
One practical consideration in price-break problems is that the price reduction from volume purchases frequently makes it seemingly economical to order amounts larger than the
Qopt. Thus, when applying the model, we must be particularly careful to obtain a valid estimate of product obsolescence and warehousing costs.
INVENTORY PLANNING AND ACCURACY
LO 20–3
Analyze inventory using
the Pareto principle.
ABC inventory
classification
Divides inventory into
dollar volume categories
that map into strategies
appropriate for the
category.
Maintaining inventory through counting, placing orders, receiving stock, and so on takes personnel time and costs money. When there are limits on these resources, the logical move is to
try to use the available resources to control inventory in the best way. In other words, focus on
the most important items in inventory.
In the nineteenth century, Villefredo Pareto, in a study of the distribution of wealth in
Milan, found that 20 percent of the people controlled 80 percent of the wealth. This logic of
the few having the greatest importance and the many having little importance has been broadened to include many situations and is termed the Pareto principle.3 This is true in our everyday lives (most of our decisions are relatively unimportant, but a few shape our future) and is
certainly true in inventory systems (where a few items account for the bulk of our investment).
Any inventory system must specify when an order is to be placed for an item and how
many units to order. Most inventory control situations involve so many items that it is not
practical to model and give thorough treatment to each item. To get around this problem, the
ABC inventory classification scheme divides inventory items into three groupings: high dollar volume (A), moderate dollar volume (B), and low dollar volume (C). Dollar volume is a
measure of importance; an item low in cost but high in volume can be more important than a
high-cost item with low volume.
A B C Cla ssif icatio n
If the annual usage of items in inventory is listed according to dollar volume, generally, the
list shows that a small number of items account for a large dollar volume and that a large number of items account for a small dollar volume. Exhibit 20.11A illustrates the relationship.
The ABC approach divides this list into three groupings by value: A items constitute
roughly the top 15 percent of the items, B items the next 35 percent, and C items the last
50 percent. From observation, it appears that the list in Exhibit 20.11A can be meaningfully
grouped with A including 20 percent (2 of the 10), B including 30 percent, and C including 50
percent. These points show clear delineations between sections. The result of this segmentation is shown in Exhibit 20.11B and plotted in Exhibit 20.11C.
Segmentation may not always occur so neatly. The objective, though, is to try to separate
the important from the unimportant. Where the lines actually break depends on the particular
inventory under question and on how much personnel time is available. (With more time, a
firm could define larger A or B categories.)
The purpose of classifying items into groups is to establish the appropriate degree of control over each item. On a periodic basis, for example, class A items may be more clearly controlled with weekly ordering, B items may be ordered biweekly, and C items may be ordered
monthly or bimonthly. Note that the unit cost of items is not related to their classification.
An A item may have a high dollar volume through a combination of either low cost and high
usage or high cost and low usage. Similarly, C items may have a low dollar volume because of
either low demand or low cost. In an automobile service station, gasoline would be an A item
with daily or weekly replenishment; tires, batteries, oil, grease, and transmission fluid may
be B items and ordered every two to four weeks; and C items would consist of valve stems,
windshield wiper blades, radiator caps, hoses, fan belts, oil and gas additives, car wax, and so
forth. C items may be ordered every two or three months or even be allowed to run out before
reordering because the penalty for stockout is not serious.
Sometimes an item may be critical to a system if its absence creates a sizable loss. In this
case, regardless of the item’s classification, sufficiently large stocks should be kept on hand to
prevent runout. One way to ensure closer control is to designate this item an A or a B, forcing
it into the category even if its dollar volume does not warrant such inclusion.
Inventory Management
ex hibit 20.11
Chapter 20
A. Annual Usage of Inventory by Value
Item Number
Annual Dollar Usage
Percentage of Total Value
22
$ 95,000
40.69%
68
75,000
32.13
27
25,000
10.71
03
15,000
6.43
82
13,000
5.57
54
7,500
3.21
36
1,500
0.64
19
800
0.34
23
425
0.18
41
225
0.10
$233,450
100.00%
B. ABC Grouping of Inventory Items
Classification
Item Number
Annual Dollar Usage
Percentage of Total
A
22, 68
$170,000
B
27, 03, 82
53,000
22.7
72.8%
C
54, 36, 19, 23, 41
10,450
4.5
$233,450
100.0%
C. ABC Inventory Classification (inventory value for each group versus the group’s portion
of the total list)
100
80
Percentage
of total
inventory
value
60
40
A items
20
0
B items
20
40
C items
60
80
100
Percentage of total list of different stock items
I n ve n t or y Accur a cy a nd C ycle C o u n tin g
Inventory records usually differ from the actual physical count; inventory accuracy refers to how
well the two agree. Companies such as Walmart understand the importance of inventory accuracy
and expend considerable effort ensuring it. The question is, “How much error is acceptable?” If
the record shows a balance of 683 of part X, and an actual count shows 652, is this within reason?
Suppose the actual count shows 750, an excess of 67 over the record. Is this any better?
Every production system must have agreement, within some specified range, between what
the record says is in inventory and what actually is in inventory. There are many reasons why
records and inventory may not agree. For example, an open stockroom area allows items to
be removed for both legitimate and unauthorized purposes. The legitimate removal may have
been done in a hurry and simply not recorded. Sometimes parts are misplaced, turning up
months later. Parts are often stored in several locations, but records may be lost or the location
recorded incorrectly. Sometimes stock replenishment orders are recorded as received, when
in fact they never were. Occasionally, a group of parts is recorded as removed from inventory,
but the customer order is canceled and the parts are replaced in inventory without canceling
the record. To keep the production system flowing smoothly without parts shortages and efficiently without excess balances, records must be accurate.
539
540
Supply and Demand Planning and Control
Section 4
A sales clerk at Tokyo’s
Mitsukoshi department
store reads an RFID tag
on jeans to check stock.
Mitsukoshi and Japan’s
electronic giant Fujitsu
partnered to use RFID to
improve stock control
and customer service.
© AFP/Getty Images
Cycle counting
A physical inventorytaking technique in which
inventory is counted on a
frequent basis rather than
once or twice a year.
How can a firm keep accurate, up-to-date records? Using bar codes and RFID tags is important to minimizing errors caused by inputting wrong numbers in the system. It is also important to keep the storeroom locked. If only storeroom personnel have access, and one of their
measures of performance for personnel evaluation and merit increases is record accuracy, there
is a strong motivation to comply. Every location of inventory storage, whether in a locked
storeroom or on the production floor, should have a recordkeeping mechanism. A second way
is to convey the importance of accurate records to all personnel and depend on them to assist in
this effort. (It all boils down to this: Put a fence that goes all the way to the ceiling around the
storage area so that workers cannot climb over to get parts; put a lock on the gate and give one
person the key. Nobody can pull parts without having the transaction authorized and recorded.)
Another way to ensure accuracy is to count inventory frequently and match this against
records. A widely used method is called cycle counting.
Cycle counting a physical inventory-taking technique in which inventory is counted frequently rather than once or twice a year. The key to effective cycle counting and, therefore, to
accurate records lies in deciding which items are to be counted, when, and by whom.
Virtually all inventory systems these days are computerized. The computer can be programmed to produce a cycle count notice in the following cases:
1.
2.
3.
4.
When the record shows a low or zero balance on hand. (It is easier to count fewer items.)
When the record shows a positive balance but a backorder was written (indicating a
discrepancy).
After some specified level of activity.
To signal a review based on the importance of the item (as in the ABC system) such
as in the following table:
Annual Dollar Usage
Review Period
$10,000 or more
30 days or less
$3,000–$10,000
45 days or less
$250–$3,000
90 days or less
Less than $250
180 days or less
Inventory Management
Chapter 20
541
The easiest time for stock to be counted is when there is no activity in the stockroom or on
the production floor. This means on the weekends or during the second or third shift, when
the facility is less busy. If this is not possible, more careful logging and separation of items
are required to count inventory while production is going on and transactions are occurring.
The counting cycle depends on the available personnel. Some firms schedule regular stockroom personnel to do the counting during lulls in the regular working day. Other companies
hire private firms that come in and count inventory. Still other firms use full-time cycle counters who do nothing but count inventory and resolve differences with the records. Although
this last method sounds expensive, many firms believe that it is actually less costly than the
usual hectic annual inventory count generally performed during the two- or three-week annual
vacation shutdown.
The question of how much error is tolerable between physical inventory and records has
been much debated. Some firms strive for 100 percent accuracy, whereas others accept a
1, 2, or 3 percent error. The accuracy level often recommended by experts is ±0.2 percent
for A items, ±1 percent for B items, and ±5 percent for C items. Regardless of the specific
accuracy decided on, the important point is that the level be dependable so that safety stocks
may be provided as a cushion. Accuracy is important for a smooth production process so that
customer orders can be processed as scheduled and not held up because of unavailable parts.
Concept Connections
LO 20–1 Explain how inventory is used and understand what it costs.
Summary
∙ Inventory is expensive mainly due to storage, obsolescence, insurance, and the value of the money invested.
∙ This chapter explains models for controlling inventory that are appropriate when it is difficult to predict exactly what demand will be for an item in the
future and it is desired to have the item available from
“stock.”
∙ The basic decisions that need to be made are: (1) when
should an item be ordered, and (2) how large should
the order be.
∙ The main costs relevant to these models are: (1) the
cost of the item itself, (2) the cost to hold an item in
inventory, (3) setup costs, (4) ordering costs, and (5)
costs incurred when an item runs short.
Key Terms
Inventory The stock of any item or resource used in an
organization.
Independent demand The demands for these items are
unrelated to each other, or to activities that can be predicted with certainty.
Dependent demand The need for an item is a direct
result of the need for some other item, usually an item
of which it is a part. Also, when the demand for the item
can be predicted with accuracy due to a schedule or specific activitity.
LO 20–2 Analyze how different inventory control systems work.
Summary
∙ An inventory system provides a specific operating
policy for managing items to be in stock. Other than
defining the timing and sizing of orders, the system
needs to track the exact status of these orders (Have
the orders been received by the supplier? Have they
been shipped? On which date is each expected? And
so on.).
∙ Single-period model—When an item is purchased
only one time and it is expected that it will be used
and then not reordered, the single-period model is
appropriate.
∙ Multiple-period models—When the item will be reordered and the intent is to maintain the item in stock,
multiple-period models are appropriate.
542
Supply and Demand Planning and Control
Section 4
∙ There are two basic types of multiple-period models,
with the key distinction being what triggers the timing
of the order placement.
∙ With the fixed–order quantity model, an order is
placed when inventory drops to a low level called the
reorder point.
∙ With the fixed–time period model, orders are placed
at fixed intervals of time, say, every two weeks. The
order quantity varies for each order.
∙ Safety stock is extra inventory that is carried for protection in case the demand for an item is greater than
expected. Statistics are used to determine an appropriate amount of safety stock to carry based on the probability of stocking out.
∙ Inventory turn measures the expected number of times
that average inventory is replaced over a year. It can be
calculated in aggregate using average inventory levels
or on an individual item basis.
Key Terms
Single-period problem Answers the question of how
much to order when an item is purchased only one
time and it is expected that it will be used and then not
reordered.
Fixed–order quantity model (Q-model) An inventory
control model where the amount requisitioned is fixed
and the actual ordering is triggered by inventory dropping to a specified level of inventory.
Fixed–time period model (P-model) An inventory control model that specifies inventory is ordered at the end
of a predetermined time period. The interval of time
between orders is fixed and the order quantity varies.
Inventory position The amount on hand plus onorder minus backordered quantities. In the case where
inventory has been allocated for special purposes,
Key Formulas
[20.1]
​C​  u​​
​P ≤ _____
​
​​
​C​  o​​ + ​C​  u​​
the inventory position is reduced by these allocated
amounts.
Optimal order quantity (Qopt) This order size minimizes
total annual cost.
Reorder point (R) An order is placed when inventory
drops to this level.
Safety stock The amount of inventory carried in addition to the expected demand.
Inventory turn The cost of goods sold divided by the total
average value of inventory. A measure of the expected
number of times that inventory is replaced each year.
Price-break model This model is useful for finding the
order quantity of an item when the price of the item varies with the order size.
[20.7]
[20.2] Inventory position = On-hand + On-order –
Backorder
[20.3]
[20.4]
Q
D ​ S + ​ __
​​TC = DC + ​ __
​ H​​
Q
2
[20.5]
​​R = d ​
​ ¯L​​
[20.6]
​ ¯L + z ​σ​  L​​
​​R = d ​
[20.11]
___________
[20.8]
n
​ ​∑
​​​​​ ​​ ​d​  ​​ − ​ d¯​​​​)​​​​  2​ ​
√
i=1 ( i
​d ​
​  ¯ = __________
​
n ​​ ​​
____
​​​Q​  opt​​ = ​ ____
​  2DS
​ ​​​
H
√
​∑ n ​​​ ​d​  i​​
​ d¯​ = ______
​  i=1
n ​
[20.9]
[20.10]
____________
​​​σL​  ​​ = ​√
​σ​  21​ + ​
​  σ​  22​ ​  + . . . +​σ​  2L ​ ​​  ​​
Safety stock = z​σT​ + L
Inventory currently
Average demand
Order
Safety
on
hand (plus on​
​ ​ = ​
​ ​​+ ​
​​ −  ​
​
​​
over
the
​​quantity
​  ​  vulnerable period
​
​  stock
​  ​
​
​  ​​​
order, if any)
q
​=       ​ d¯​​(​​T + L​)​​​
+   z ​σ​  ​​ −                I
​
Inventory Management
√
[20.12]
[20.13]
_____
T+L
[20.14]
​​​σ​  T+L​​ = ​ ​  ∑​​​ ​σ​  2d​ ​​  ​​
i=1
[20.15]
​​Average inventory value= (​​ ​​Q ∕ 2 + SS​)​​​C​​
Chapter 20
543
DC
D
​ = ______
​
​​​
​​ Inventory turn= ​ _________
(​​ ​​Q ∕ 2 + SS​)​​​C Q ∕ 2 + SS
____
​​Q = ​ ____
​  2DS ​ ​​​
iC
√
LO 20–3 Analyze inventory using the Pareto principle.
Summary
∙ Most inventory control systems are so large that it is
not practical to model and give a thorough treatment
to each item. In these cases, it is useful to categorize
items according to their yearly dollar value.
∙ A simple A, B, C categorization where A items are
the high annual dollar value items, B items are the
medium dollar value items, and C items are the low
dollar value items is useful. This categorization can
be used as a measure of the relative importance of
an item.
∙ Typically, A items are roughly the top 15 percent of
the items and represent 80 percent of the yearly dollar
value. B items would be the next 35 percent and make
up around 15 percent of the yearly dollar value. The
C items would be the last 50 percent of the item, and
have only 5 percent of the yearly dollar value.
∙ Cycle counting is a useful method for scheduling the
audit of each item carried in inventory. Companies
audit their inventory at least yearly to ensure accuracy
of the records.
Key Terms
ABC inventory classification Divides inventory into dol-
Cycle counting A physical inventory-taking technique
lar volume categories that map into strategies appropriate for the category.
in which inventory is counted on a frequent basis rather
than once or twice a year.
Solved Problems
LO 20–2
SOLVED PROBLEM 1
A product is priced to sell at $100 per unit, and its cost is constant at $70 per unit. Each unsold
unit has a salvage value of $20. Demand is expected to range between 35 and 40 units for the
period; 35 definitely can be sold and no units over 40 will be sold. The demand probabilities and
the associated cumulative probability distribution (P) for this situation are shown as follows.
Number
of Units
Demanded
Probability
of This
­Demand
Cumulative
Probability
35
36
37
38
39
40
0.10
0.15
0.25
0.25
0.15
0.10
0.10
0.25
0.50
0.75
0.90
1.00
How many units should be ordered?
Solution
The cost of underestimating demand is the loss of profit, or Cu = $100 − $70 = $30 per unit.
The cost of overestimating demand is the loss incurred when the unit must be sold at salvage
value, Co = $70 − $20 = $50.
The optimal probability of not being sold is
​C​u​
​P ≤ _____
​
​= _____
​ 30 ​= .375​​
​C​o​+ ​C​u​ 50 + 30
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Supply and Demand Planning and Control
From the distribution data given, this corresponds to the 37th unit.
The following is a full marginal analysis for the problem. Note that the minimum cost
occurs when 37 units are purchased.
Number of Units Purchased
Units Demanded
Probability
35
36
37
38
39
40
35
0.1
0
50
100
150
200
250
36
0.15
30
0
50
100
150
200
37
0.25
60
30
0
50
100
150
38
0.25
90
60
30
0
50
100
39
0.15
120
90
60
30
0
50
40
0.1
150
120
90
60
30
0
75
53
43
53
83
125
Total cost
SOLVED PROBLEM 2
Items purchased from a vendor cost $20 each, and the forecast for next year’s demand is 1,000
units. If it costs $5 every time an order is placed for more units, and the storage cost is $4 per
unit per year, answer the following questions.
a. What quantity should be ordered each time?
b. What is the total ordering cost for a year?
c. What is the total storage cost for a year?
Solution
a. The quantity to be ordered each time is
____
________
2​​(​1,000​)​5
​ = ​ ____
Q
​2DS ​ = ​ _______
​
​ = 50 units​
√
H
√
4
b. The total ordering cost for a year is
1,000
__
​
​(​$5​)​= $100​​
​D ​S = _____
Q
50
c. The storage cost for a year is
Q
__
​ ​H = __
​50 ​(​$4​)​= $100​
2
2
SOLVED PROBLEM 3
Daily demand for a product is 120 units, with a standard deviation of 30 units. The review
period is 14 days and the lead time is 7 days. At the time of review, 130 units are in stock. If
only a 1 percent risk of stocking out is acceptable, how many units should be ordered?
Solution
___________
______
​σ​T+L​ = ​√ (14 + 7 ) ​(30 )​​2​ = ​√ 18,900 ​= 137.5
z = 2.33
​​
​
​ L ) + z ​σ​T+L​− I​
​ ​​​
q
=​  d ​
​  ¯(T +
​ = 120(14 + 7 ) + 2.33(137.5 ) − 130
​ = 2,710 units
SOLVED PROBLEM 4
A company currently has 200 units of a product on-hand that it orders every two weeks when
the salesperson visits the premises. Demand for the product averages 20 units per day with a
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545
standard deviation of 5 units. Lead time for the product to arrive is seven days. Management
has a goal of a 95 percent probability of not stocking out for this product.
The salesperson is due to come in late this afternoon when 180 units are left in stock
(assuming that 20 are sold today). How many units should be ordered?
Solution
Give I = 180, T = 14, L = 7, d = 20
______
​σT+L
​ ​ = ​√ 21 ​(​5​)​2​ = 23
z = 1.64
​
​  ​ ​
​​
​
​
​
q = d ​
​  ¯(​ ​T + L​)​+ z ​σT+L
​ ​− I
​​
​ = 20​​(​14 + 7​)​+ 1.64​​(​23​)​− 180
q = 278 units
SOLVED PROBLEM 5
Sheet Metal Industries Inc. (SMI) is a Tier 1 supplier to various industries that use components made from sheet metal in their final products. Manufacturers of desktop computers and
electronic devices are its primary customers. SMI orders a relatively small number of different raw sheet metal products in very large quantities. The purchasing department is trying
to establish an ordering policy that will minimize total costs while meeting the needs of the
firm. One of the highest volume items it purchases comes in precut sheets direct from the steel
processor. Forecasts based on historical data indicate that SMI will need to purchase 200,000
sheets of this product on an annual basis. The steel producer has a minimum order quantity of
1,000 sheets, and offers a sliding price scale based on the quantity in each order, as follows.
Order Quantity
Unit Price
1,000–9,999
$2.35
10,000–29,999
$2.20
30,000 +
$2.15
The purchasing department estimates that it costs $300 to process each order, and SMI
has an inventory carrying cost equal to 15 percent of the value of inventory.
Based on this information, use the price-break model to determine an optimal order
quantity.
Solution
The first step is to take the information in the problem and assign it to the proper notation in
the model.
D = 200,000 units (annual demand)
S = $300 to place and process each order
I = 15 percent of the item cost
C = cost per unit, based on the order quantity Q, as shown in the table
Next, solve the economic order size at each price point starting with the lowest unit price.
Stop when you reach a feasible Q.
____________
2 * 200,000 * 300
​Q​$2.15​= ​ ____________
​
​ = 19,290 (infeasible)​
.15 * 2.15
√
The EOQ at $2.15 is not feasible for that price point. The best quantity to order at that
price point is therefore the minimum feasible quantity of 30,000.
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Supply and Demand Planning and Control
Section 4
____________
2 * 200,000 * 300
​Q​$2.20​= ​ ____________
​  ​ = 19,069 ​(​feasible​)​
.15 * 2.20
√
The EOQ at $2.20 is feasible, therefore the best quantity to order at that price point is
the EOQ of 19,069. Because we found a feasible EOQ at this price point, we do not need to
consider any higher price points. The two ordering policies to consider are: Order 30,000
sheets each time at $2.15 apiece, or order 19,069 sheets each time at $2.20 each. The question
is whether the purchase price savings at the $2.15 price point will offset the higher holding
costs that would result from the higher ordering quantity. To answer this question, compute
the total cost of each option.
200,000
30,000
TC ​Q=30,000​= 200,000 * $2.15 + ______
​
​($300 ) + _____
​
​(.15 )($2.15 ) ≈ $436,837
30,000
2
​
​
200,000
19,069
______
_____
T ​C​Q=19,069​= 200,000 * $2.20 + ​
​($300 ) + ​
​(.15 )($2.20 ) ≈ $446,293
2
19,069
The lowest total annual cost comes when ordering 30,000 units at $2.15, so that would be
the best ordering policy. Are you surprised that the 5-cent difference in unit price would make
such a difference in total cost? When dealing in large volumes, even tiny price changes can
have a significant impact on the big picture.
Discussion Questions
LO20–1
LO20–2
LO20–3
1. Distinguish between dependent and independent demand in a McDonald’s restaurant, in
an integrated manufacturer of personal copiers, and in a pharmaceutical supply house.
2. Distinguish between in-process inventory, safety stock inventory, and seasonal inventory.
3. Discuss the nature of the costs that affect inventory size. For example:
a. How does shrinkage (stolen stock) contribute to the cost of carrying inventory? How
can this cost be reduced?
b. How does obsolescence contribute to the cost of carrying inventory? How can this
cost be reduced?
4. Under which conditions would a plant manager elect to use a fixed–order quantity model
as opposed to a fixed–time period model? What are the disadvantages of using a fixed–
time period ordering system?
5. What two basic questions must be answered by an inventory control decision rule?
6. Discuss the assumptions that are inherent in production setup cost, ordering cost, and carrying costs. How valid are they?
7. “The nice thing about inventory models is that you can pull one off the shelf and apply it
so long as your cost estimates are accurate.” Comment.
8. Which type of inventory system would you use in the following situations?
a. Supplying your kitchen with fresh food
b. Obtaining a daily newspaper
c. Buying gas for your car
To which of these items do you impute the highest stock-out cost?
9. What is the purpose of classifying items into groups, as the ABC classification does?
10. When cycle counting inventory, why do experts recommend a lower acceptable error
tolerance for A items than B or C items?
Objective Questions
LO20–1
1. What is the term used to refer to inventory while in distribution—that is, being moved
within the supply chain?
2. Almost certainly you have seen vending machines being serviced on your campus and
elsewhere. On a predetermined schedule, the vending company checks each machine and
fills it with various products. This is an example of which category of inventory model?
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547
3. To support the manufacture of desktop computers for its customers, Dell needs to order
all the parts that go into the computer, such as hard drives, motherboards, and memory
modules. Obviously, the demand for these items is driven by the production schedule for
the computers. What is the term used to describe demand for these parts?
4. The local supermarket buys lettuce each day to ensure really fresh produce. Each
morning, any lettuce that is left from the previous day is sold to a dealer that resells it
to farmers who use it to feed their animals. This week, the supermarket can buy fresh
lettuce for $4.00 a box. The lettuce is sold for $10.00 a box and the dealer that sells
old lettuce is willing to pay $1.50 a box. Past history says that tomorrow’s demand
for lettuce averages 250 boxes with a standard deviation of 34 boxes. How many
boxes of lettuce should the supermarket purchase tomorrow? (Answer available in
Appendix D)
5. Next week, Super Discount Airlines has a flight from New York to Los Angeles that
will be booked to capacity. The airline knows from past history that an average of 25
customers (with a standard deviation of 15) cancel their reservation or do not show
for the flight. Revenue from a ticket on the flight is $125. If the flight is overbooked,
the airline has a policy of getting the customer on the next available flight and giving
the person a free round-trip ticket on a future flight. The cost of this free round-trip
ticket averages $250. Super Discount considers the cost of flying the plane from New
York to Los Angeles a sunk cost. By how many seats should Super Discount overbook
the flight?
6. Solve the newsperson problem. What is the optimal order quantity?
Probability
0.2
0.1
0.1
0.2
0.3
0.1
Value
1
2
3
4
5
6
Purchase cost c = 15
Selling price p = 25
Salvage value v = 10
7. Wholemark is an Internet order business that sells one popular New Year’s greeting card once a year. The cost of the paper on which the card is printed is $0.05 per
card, and the cost of printing is $0.15 per card. The company receives $2.15 per card
sold. Because the cards have the current year printed on them, unsold cards have no
­salvage value. Its customers are from the four areas: Los Angeles, Santa Monica,
Hollywood, and Pasadena. Based on past data, the number of customers from each of
the four regions is normally distributed with a mean of 2,000 and a standard deviation of 500. (Assume these four are independent.) What is the optimal production
quantity for the card?
8. Lakeside Bakery bakes fresh pies every morning. The daily demand for its apple pies is a
random variable with (discrete) distribution, based on past experience, given by
Demand
Probability
5
10%
10
15
20
25
20%
25%
25%
15%
30
5%
ach apple pie costs the bakery $6.75 to make and is sold for $17.99. Unsold apple pies
E
at the end of the day are purchased by a nearby soup kitchen for 99 cents each. Assume
no goodwill cost.
a. If the company decided to bake 15 apple pies each day, what would be its expected
profit?
b. Based on the demand distribution given, how many apple pies should the company
bake each day to maximize its expected profit?
9. Sally’s Silk Screening produces specialty T-shirts that are primarily sold at special
events. She is trying to decide how many to produce for an upcoming event. During the
event, Sally can sell T-shirts for $20 apiece. However, when the event ends, any unsold
548
Section 4
Supply and Demand Planning and Control
T-shirts are sold for $4 each. It costs Sally $8 to make a specialty T-shirt. Sally’s estimate
of demand is the following:
Demand
Probability
300
.05
400
.10
500
.40
600
.30
700
.10
800
.05
a. What is the service rate (or optimal fractile)?
b. How many T-shirts should she produce for the upcoming event?
10. You are a newsvendor selling the San Pedro Times every morning. Before you get to
work, you go to the printer and buy the day’s paper for $0.25 a copy. You sell a copy of
the San Pedro Times for $1.00. Daily demand is distributed normally with mean = 250
and standard deviation = 50. At the end of each morning, any leftover copies are worthless and they go to a recycle bin.
a. How many copies of the San Pedro Times should you buy each morning?
b. Based on part (a), what is the probability that you will run out of stock?
11. Famous Albert prides himself on being the Cookie King of the West. Small, freshly
baked cookies are the specialty of his shop. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand,
he estimates demand for cookies as the following:
Demand
Probability of Demand
1,800 dozen
0.05
2,000
0.10
2,200
0.20
2,400
0.30
2,600
0.20
2,800
0.10
3,000
0.05
Each dozen sells for $0.69 and costs $0.49, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.29 and sold the
following day as day-old merchandise.
a. Construct a table showing the profits or losses for each possible quantity.
b. What is the optimal number of cookies to make?
c. Solve this problem by using marginal analysis.
12. Ray’s Satellite Emporium wishes to determine the best order size for its best-selling satellite dish (Model TS111). Ray has estimated the annual demand for this model at 1,000
units. His cost to carry one unit is $100 per year per unit, and he has estimated that each
order costs $25 to place. Using the EOQ model, how many should Ray order each time?
13. Dunstreet’s Department Store would like to develop an inventory ordering policy with
a 95 percent probability of not stocking out. To illustrate your recommended procedure,
use as an example the ordering policy for white percale sheets.
Demand for white percale sheets is 5,000 per year. The store is open 365 days per year.
Every two weeks (14 days) inventory is counted and a new order is placed. It takes 10
days for the sheets to be delivered. Standard deviation of demand for the sheets is 5 per
day. There are currently 150 sheets on-hand.
How many sheets should you order?
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549
14. Charlie’s Pizza orders all of its pepperoni, olives, anchovies, and mozzarella cheese to be
shipped directly from Italy. An American distributor stops by every four weeks to take
orders. Because the orders are shipped directly from Italy, they take three weeks to arrive.
Charlie’s Pizza uses an average of 150 pounds of pepperoni each week, with a standard
deviation of 30 pounds. Charlie’s prides itself on offering only the best-quality ingredients and a high level of service, so it wants to ensure a 98 percent probability of not
stocking out on pepperoni.
Assume that the sales representative just walked in the door and there are currently
500 pounds of pepperoni in the walk-in cooler. How many pounds of pepperoni would
you order? (Answer in Appendix D)
15. Given the following information, formulate an inventory management system. The item
is demanded 50 weeks a year.
Parameter
Value
Item cost
$10.00
Order cost
$250.00/order
Annual holding cost
33% of item cost
Annual demand
25,750 units
Average weekly demand
515/week
Standard deviation of weekly demand
25 units
Lead time
1 week
Service probability
95%
a. State the order quantity and reorder point.
b. Determine the annual holding and order costs.
c. If a price break of $50 per order was offered for purchase quantities of over 2,000,
would you take advantage of it? How much would you save annually?
16. Lieutenant Commander Data is planning to make his monthly (every 30 days) trek to
Gamma Hydra City to pick up a supply of isolinear chips. The trip will take Data about
two days. Before he leaves, he calls in the order to the GHC Supply Store. He uses chips
at an average rate of 5 per day (seven days per week) with a standard deviation of demand
of 1 per day. He needs a 98 percent service probability. If he currently has 35 chips in
inventory, how many should he order? What is the most he will ever have to order?
17. Jill’s Job Shop buys two parts (Tegdiws and Widgets) for use in its production system
from two different suppliers. The parts are needed throughout the entire 52-week year.
Tegdiws are used at a relatively constant rate and are ordered whenever the remaining
quantity drops to the reorder level. Widgets are ordered from a supplier who stops by
every three weeks. Data for both products are as follows: (Answers in Appendix D)
Item
Tegdiw
Widget
Annual demand
10,000
5,000
Holding cost (% of item cost)
20%
20%
Setup or order cost
$150.00
$25.00
Lead time
4 weeks
1 week
Safety stock
55 units
5 units
Item cost
$10.00
$2.00
a. What is the inventory control system for Tegdiws? That is, what is the reorder quantity
and what is the reorder point?
b. What is the inventory control system for Widgets?
18. Demand for an item is 1,000 units per year. Each order placed costs $10; the annual cost
to carry items in inventory is $2 each. In what quantities should the item be ordered?
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Section 4
Supply and Demand Planning and Control
19. The annual demand for a product is 15,600 units. The weekly demand is 300 units with
a standard deviation of 90 units. The cost to place an order is $31.20, and the time from
ordering to receipt is four weeks. The annual inventory carrying cost is $0.10 per unit.
Find the reorder point necessary to provide a 98 percent service probability.
Suppose the production manager is asked to reduce the safety stock of this item by
50 percent. If she does so, what will the new service probability be?
20. Daily demand for a product is 100 units, with a standard deviation of 25 units. The review
period is 10 days and the lead time is 6 days. At the time of review, there are 50 units in
stock. If 98 percent service probability is desired, how many units should be ordered?
21. Item X is a standard item stocked in a company’s inventory of component parts. Each
year, the firm, on a random basis, uses about 2,000 of item X, which costs $25 each. Storage costs, which include insurance and cost of capital, amount to $5 per unit of average
inventory. Every time an order is placed for more of item X, it costs $10.
a. Whenever item X is ordered, what should the order size be?
b. What is the annual cost for ordering item X?
c. What is the annual cost for storing item X?
22. Annual demand for a product is 13,000 units; weekly demand is 250 units with a standard
deviation of 40 units. The cost of placing an order is $100, and the time from ordering to
receipt is four weeks. The annual inventory carrying cost is $0.65 per unit. To provide a
98 percent service probability, what must the reorder point be?
Suppose the production manager is told to reduce the safety stock of this item by
100 units. If this is done, what will the new service probability be?
23. Gentle Ben’s Bar and Restaurant uses 5,000 quart bottles of an imported wine each year.
The effervescent wine costs $3 per bottle and is served only in whole bottles because it
loses its bubbles quickly. Ben figures that it costs $10 each time an order is placed, and
holding costs are 20 percent of the purchase price. It takes three weeks for an order to
arrive. Weekly demand is 100 bottles (closed two weeks per year) with a standard deviation of 30 bottles.
Ben would like to use an inventory system that minimizes inventory cost and will provide a 95 percent service probability.
a. What is the economic quantity for Ben to order?
b. At what inventory level should he place an order?
24. Retailers Warehouse (RW) is an independent supplier of household items to department
stores. RW attempts to stock enough items for a 98 percent service probability.
A stainless steel knife set is one item it stocks. Demand (2,400 sets per year) is relatively stable over the entire year. Whenever new stock is ordered, a buyer must ensure
that numbers are correct for stock on-hand and then phone in a new order. The total cost
involved to place an order is about $5. RW figures that holding inventory in stock and
paying for interest on borrowed capital, insurance, and so on, add up to about $4 holding cost per unit per year.
Analysis of the past data shows that the standard deviation of demand from retailers
is about four units per day for a 365-day year. Lead time to get the order is seven days.
a. What is the economic order quantity?
b. What is the reorder point?
25. Daily demand for a product is 60 units with a standard deviation of 10 units. The review
period is 10 days, and lead time is 2 days. At the time of review, there are 100 units in
stock. If 98 percent service probability is desired, how many units should be ordered?
26. University Drug Pharmaceuticals orders its antibiotics every two weeks (14 days) when
a salesperson visits from one of the pharmaceutical companies. Tetracycline is one of its
most prescribed antibiotics, with an average daily demand of 2,000 capsules. The standard deviation of daily demand was derived from examining prescriptions filled over the
past three months and was found to be 800 capsules. It takes five days for the order to
arrive. University Drug would like to satisfy 99 percent of the prescriptions. The salesperson just arrived, and there are currently 25,000 capsules in stock.
How many capsules should be ordered?
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27. Sarah’s Muffler Shop has one standard muffler that fits a large variety of cars. Sarah
wishes to establish a reorder point system to manage inventory of this standard muffler.
Use the following information to determine the best order size and the reorder point.
Annual demand
3,500 mufflers
Ordering cost
$50 per order
Standard deviation of
daily demand
6 mufflers per working
day
Service probability
90%
Item cost
$30 per muffler
Lead time
2 working days
Annual holding cost
25% of item value
Working days
300 per year
28. After graduation, you decide to go into a partnership in an office supply store that has
existed for a number of years. Walking through the store and stockrooms, you find a great
discrepancy in service levels. Some spaces and bins for items are completely empty; others have supplies that are covered with dust and have obviously been there a long time.
You decide to take on the project of establishing consistent levels of inventory to meet
customer demands. Most of your supplies are purchased from just a few distributors that
call on your store once every two weeks.
You choose, as your first item for study, computer printer paper. You examine the
sales records and purchase orders and find that demand for the past 12 months was 5,000
boxes. Using your calculator, you sample some days’ demands and estimate that the standard deviation of daily demand is 10 boxes. You also search out these figures:
Cost per box of paper: $11
Desired service probability: 98 percent
Store is open every day.
Salesperson visits every two weeks.
Delivery time following visit is three days.
sing your procedure, how many boxes of paper would be ordered if, on the day the
U
salesperson calls, 60 boxes are on-hand?
29. A distributor of large appliances needs to determine the order quantities and reorder
points for the various products it carries. The following data refer to a specific refrigerator in its product line.
Cost to place an order
$100/order
Holding cost
20 percent of product cost per year
Cost of refrigerator
$500/unit
Annual demand
500 units
Standard deviation of demand during lead time
10 units
Lead time
7 days
Consider an even daily demand and a 365-day year.
a. What is the economic order quantity?
b. If the distributor wants a 97 percent service probability, what reorder point, R, should
be used?
30. It is your responsibility, as the new head of the automotive section of Nichols Department
Store, to ensure that reorder quantities for the various items have been correctly established. You decide to test one item and choose Michelin tires, XW size 185 × 14 BSW. A
perpetual inventory system has been used, so you examine this, as well as other records,
and come up with the following data.
Cost per tire
$35 each
Holding cost
20 percent of tire cost per year
Demand
1,000 per year
Ordering cost
$20 per order
Standard deviation of daily demand
3 tires
Delivery lead time
4 days
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ecause customers generally do not wait for tires but go elsewhere, you decide on a serB
vice probability of 98 percent. Assume the demand occurs 365 days per year.
a. Determine the order quantity.
b. Determine the reorder point.
31. UA Hamburger Hamlet (UAHH) places a daily order for its high-volume items (hamburger patties, buns, milk, and so on). UAHH counts its current inventory on-hand once
per day and phones in its order for delivery 24 hours later. Determine the number of hamburgers UAHH should order for the following conditions:
Average daily demand
600
Standard deviation of demand
100
Desired service probability
99%
Hamburger inventory
800
32. A local service station is open 7 days per week, 365 days per year. Sales of 10W40 grade
premium oil average 20 cans per day. Inventory holding costs are $0.50 per can per year.
Ordering costs are $10 per order. Lead time is two weeks. Backorders are not practical—
the motorist drives away.
a. Based on these data, choose the appropriate inventory model and calculate the economic order quantity and reorder point. Describe in a sentence how the plan would
work. Hint: Assume demand is deterministic.
b. The boss is concerned about this model because demand really varies. The standard
deviation of demand was determined from a data sample to be 6.15 cans per day. The
manager wants a 99.5 percent service probability. Determine a new inventory plan
based on this information and the data in part (a). Use Qopt from part (a).
33. Dave’s Auto Supply custom mixes paint for its customers. The shop performs a weekly
inventory count of the main colors used for mixing paint. Determine the amount of white
paint that should be ordered using the following information:
Average weekly demand
20 gallons
Standard deviation of demand
5 gallons/week
Desired service probability
98%
Current inventory
25 gallons
Lead time
1 week
34. SY Manufacturers (SYM) is producing T-shirts in three colors: red, blue, and white. The
monthly demand for each color is 3,000 units. Each shirt requires 0.5 pound of raw cotton
that is imported from Luft-Geshfet-Textile (LGT) Company in Brazil. The purchasing
price per pound is $2.50 (paid only when the cotton arrives at SYM’s facilities) and transportation cost by sea is $0.20 per pound. The traveling time from LGT’s facility in Brazil
to the SYM facility in the United States is two weeks. The cost of placing a cotton order,
by SYM, is $100 and the annual interest rate that SYM is facing is 20 percent.
a. What is the optimal order quantity of cotton?
b. How frequently should the company order cotton?
c. Assuming that the first order is needed on April 1, when should SYM place the order?
d. How many orders will SYM place during the next year?
e. What is the resulting annual holding cost?
f. What is the resulting annual ordering cost?
g. If the annual interest cost is only 5 percent, how will it affect the annual number of
orders, the optimal batch size, and the average inventory? (You are not expected to
provide a numerical answer to this question. Just describe the direction of the change
and explain your answer.)
35. Demand for a book at Amazon.com is 250 units per week. The product is supplied to the
retailer from a factory. The factory pays $10 per unit, while the total cost of a shipment
from the factory to the retailer when the shipment size is Q is given by
Shipment cost = $50 + 2Q
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Chapter 20
Assume the annual inventory carrying cost is 20 percent.
a. What is the cost per shipment and annual holding cost per book?
b. What is the optimal shipment size?
c. What is the average throughput time?
36. Palin’s Muffler Shop has one standard muffler that fits a large variety of cars. The shop
wishes to establish a periodic review system to manage inventory of this standard muffler. Use the information in the following table to determine the optimal inventory target
level (or order-up-to level).
Annual demand
3,000 mufflers
Ordering cost
$50 per order
Standard deviation of
daily demand
6 mufflers per working
day
Service probability
90%
Item cost
$30 per muffler
Lead time
2 working days
Annual holding cost
25% of item value
Working days
300 per year
Review period
15 working days
a. What is the optimal target level (order-up-to level)?
b. If the service probability requirement is 95 percent, the optimal target level [your
answer in part (a)] will (select one):
I. Increase.
II. Decrease.
III. Stay the same.
37. Daily demand for a certain product is normally distributed, with a mean of 100 and a
standard deviation of 15. The supplier is reliable and maintains a constant lead time of
5 days. The cost of placing an order is $10 and the cost of holding inventory is $0.50 per
unit per year. There are no stock-out costs, and unfilled orders are filled as soon as the
order arrives. Assume sales occur over 360 days of the year.
Your goal here is to find the order quantity and reorder point to satisfy a 90 percent
probability of not stocking out during the lead time.
a. What type of system is the company using?
b. Find the order quantity.
c. Find the reorder point.
38. A particular raw material is available to a company at three different prices, depending on
the size of the order:
Less than 100 pounds
$20 per pound
100 pounds to 1,000 pounds
$19 per pound
More than 1,000 pounds
$18 per pound
he cost to place an order is $40. Annual demand is 3,000 units. The holding (or carryT
ing) cost is 25 percent of the material price.
What is the economic order quantity to buy each time?
39. CU, Incorporated (CUI), produces copper contacts that it uses in switches and relays.
CUI needs to determine the order quantity, Q, to meet the annual demand at the lowest
cost. The price of copper depends on the quantity ordered. Here are price-break and other
data for the problem:
Price of copper
$0.82 per pound up to 2,499 pounds
$0.81 per pound for orders between 2,500 and 5,000 pounds
$0.80 per pound for orders greater than 5,000 pounds
LO 20–3
Annual demand
50,000 pounds per year
Holding cost
20 percent per unit per year of the price of the copper
Ordering cost
$30.00
Which quantity should be ordered?
40. In the past, Taylor Industries has used a fixed–time period inventory system that involved
taking a complete inventory count of all items each month. However, increasing labor
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Section 4
Supply and Demand Planning and Control
costs are forcing Taylor Industries to examine alternative ways to reduce the amount of
labor involved in inventory stockrooms, yet without increasing other costs, such as shortage costs. Here is a random sample of 20 of Taylor’s items.
Item Number
Annual Usage
Item Number
Annual Usage
1
$1,500
11
$13,000
2
12,000
12
600
3
2,200
13
42,000
4
50,000
14
9,900
5
9,600
15
1,200
6
750
16
10,200
7
2,000
17
4,000
8
11,000
18
61,000
9
800
19
3,500
10
15,000
20
2,900
a. What would you recommend Taylor do to cut back its labor cost? (Illustrate using an
ABC plan.)
b. Item 15 is critical to continued operations. How would you recommend it be classified?
41. Alpha Products, Inc., is having a problem trying to control inventory. There is insufficient time to devote to all its items equally. The following is a sample of some items
stocked, along with the annual usage of each item expressed in dollar volume.
Item
Annual Dollar Usage
Item
Annual Dollar Usage
a
$ 7,000
k
$80,000
b
1,000
l
400
c
14,000
m
1,100
d
2,000
n
30,000
e
24,000
o
1,900
f
68,000
p
800
g
17,000
q
90,000
h
900
r
12,000
i
1,700
s
3,000
j
2,300
t
32,000
a. Can you suggest a system for allocating control time?
b. Specify where each item from the list would be placed.
42. DAT, Inc., produces digital audiotapes to be used in the consumer audio division. DAT
lacks sufficient personnel in its inventory supply section to closely control each item
stocked, so it has asked you to determine an ABC classification. Here is a sample from
the inventory records:
Item
Average Monthly
Demand
Price per Unit
Item
Average Monthly
Demand
Price per Unit
1
700
$ 6.00
2
200
4.00
6
100
$10.00
7
3,000
2.00
3
2,000
12.00
8
2,500
1.00
4
1,100
20.00
5
4,000
21.00
9
500
10.00
10
1,000
2.00
Develop an ABC classification for these 10 items.
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Chapter 20
555
Analytics Exercise: Inventory Management at Big10Sweaters.com
Big10Sweaters.com is a new company started last year
by two recent college graduates. The idea behind the
company was simple. It will sell premium logo sweaters for Big Ten colleges with one major, unique feature.
This unique feature is a special large monogram that has
the customer’s name, major, and year of graduation. The
sweater is the perfect gift for graduating students and
alumni, particularly avid football fans who want to show
support during the football season. The company is off to
a great start and had a successful first year while selling
to only a few schools. This year it plans to expand to a
few more schools and target the entire Big Ten Conference within three years.
You have been hired by Big10Sweaters.com and
need to make a good impression by making good supply chain decisions. This is your big opportunity with a
startup. There are only two people in the firm and you
were hired with the prospect of possibly becoming a principal in the future. You majored in supply chain (operations) management in school and had a great internship
at a big retailer that was getting into Internet sales. The
experience was great, but now you are on your own and
have none of the great support that the big company
had. You need to find and analyze your own data and
make some big decisions. Of course, Rhonda and Steve,
the partners who started the company, are knowledgeable
about this venture and they are going to help along the
way.
Rhonda had the idea to start the company two years
ago and talked her friend from business school, Steve,
into joining her. Rhonda is into Web marketing, has a
degree in computer science, and has been working on
completing an online MBA. She is as much an artist as a
techie. She can really make the Website sing.
Steve majored in accounting and likes to pump the
numbers. He has done a great job of keeping the books
and selling the company to some small venture capital
people in the area. Last year, he was successful in getting them to invest $2,000,000 in the company (a onetime
investment). There were some significant strings attached
to this investment in that it stipulated that only $100,000
per year could go toward paying the salary of the two
principals. The rest had to be spent on the ­
Website,
advertising, and inventory. In addition, the venture capital
company gets 25 percent of the company profits, before
taxes, during the first four years of operation, assuming
the company makes a profit.
Your first job is to focus on the firm’s inventory. The
company is centered on selling the premium sweaters to
college football fans through a Website. Your analysis is
important since a significant portion of the company’s
assets is the inventory that it carries.
The business is cyclic, and sales are concentrated
during the period leading up to the college football
season, which runs between late August and the end of
each year. For the upcoming season, the firm wants to
sell sweaters to only a few of the largest schools in the
Midwest region of the United States. In particular, it is
targeting the Ohio State University (OSU), University of
Michigan (UM), Michigan State University (MSU), Purdue University (PU), and Indiana University (IU). These
five schools have major football programs and a loyal fan
base.
The firm has considered the idea of making the
sweaters in its own factory, but for now it purchases them
from a supplier in China. The prices are great, but service is a problem because the supplier has a 20-week
lead time for each order and the minimum order size is
5,000 sweaters. The order can consist of a mix of the different logos, such as 2,000 for OSU, 1,500 for UM, 750
for MSU, 500 for PU, and 250 for IU. Within each logo
sublot, sizes are allocated based on percentages, and the
supplier suggests 20 percent X-large, 50 percent large,
20 percent medium, and 10 percent small based on its
historical data.
Once an order is received, a local subcontractor
applies the monograms and ships the sweaters to the customer. The subcontractor stores the inventory of sweaters for the company in a small warehouse area located at
their site.
This is the company’s second year of operation.
Last year, it sold sweaters for only three of the schools,
OSU, MU, and PU. It ordered the minimum 5,000
sweaters and sold all of them, but the experience was
painful because the company had too many MU sweaters and not enough for OSU fans. Last year, it ordered
2,300 OSU, 1,800 MU, and 900 PU sweaters. Of the
5,000 sweaters, 342 had to be sold at a steep discount on
eBay after the season. The company was hoping not to
do this again.
For the next year, you have collected some data relevant to the decision. Exhibit 20.12 shows cost information for the product when purchased from the supplier
in China. Here we see that the cost for each sweater,
delivered to the warehouse of our monogramming subcontractor, is $60.88. This price is valid for any quantity
we order above 5,000 sweaters. This order can be a mix
of sweaters for each of the five schools we are targeting.
The supplier needs 20 weeks to process the order, so the
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Supply and Demand Planning and Control
Section 4
exhibit 20.12
Cost Information for Big10Sweaters.com
Item
Cost
Material
$32.00
Labor
10.50
Overhead
1.25
Transportation within China
1.00
Supplier profit
8.95
Agent’s fee
2.68
Freight (ocean carrier)
1.50
Duty, insurance, etc.
3.00
Total China supplier cost
exhibit 20.13
Monogram material
5.00
Labor
8.00
Total subcontractor cost
$13.00
Total (per sweater)
$73.88
Forecast Data for Big10Sweaters.com
Average
Football Game
Attendance
Ohio State
Michigan
Purdue
Michigan State
Indiana
Penn State
Wisconsin
Iowa
Illinois
Minnesota
Northwestern
Nebraska
Total
$60.88
105,261
108,933
50,457
74,741
41,833
107,008
80,109
70,214
59,545
50,805
24,190
85,071
Rhonda’s
Forecast for
Next Year
Steve’s
Forecast for
Next Year
Market
Research
Forecast for
Next Year
Average
Forecast
Standard
Deviation
2,300
1,468
890
—
—
2,500
1,800
1,000
1,750
600
2,200
1,500
900
1,500
500
2,800
2,000
1,100
1,600
450
2,500
1,767
1,000
1,617
517
300
252
100
126
76
4,658*
7,650
6,600
7,950
7,400
430**
Last Year’s
Actual Sales
(full price)
*342 sweaters were sold through eBay for $50 each (the customer pays shipping on all orders).
_____
√ i=1
N
**Calculated assuming the demand at each school is independent​​ ​Σ​​​​σ​2i​​​
order needs to be placed around April 1 for the upcoming
football season.
Our monogramming subcontractor gets $13 for each
sweater. Shipping cost is paid by the customer when the
order is placed.
In addition to the cost data, you also have some
demand information, as shown in Exhibit 20.13. The exact
sales numbers for last year are given. Sweaters sold at full
retail price were sold for $120 each. Sweaters left over at
the end of the season were sold through eBay for $50 each
and these sweaters were not monogrammed by our subcontractor. Keep in mind that the retail sales numbers do
not accurately reflect actual demand because they stocked
out of the OSU sweaters toward the end of the season.
As for advertising the sweaters for next season,
Rhonda is committed to using the same approach used
Inventory Management
last year. The firm placed ads in the football program sold
at each game. These worked very well for reaching those
attending the games, but she realized there may be ways
to advertise that may open sales to more alumni. She has
hired a market research firm to help identify other advertising outlets but has decided to wait at least another year
to try something different.
Forecasting demand is a major problem for the company. You have asked Rhonda and Steve to predict what
they think sales might be next year. You have also asked the
market research firm to apply their forecasting tools. Data
on these forecasts are given in Exhibit 20.13. To generate
some statistics, you have averaged the forecasts and calculated the standard deviation for each school and in total.
Based on advice from the market research firm, you
have decided to use the aggregate demand forecast and
standard deviation for the aggregate demand. The aggregate demand was calculated by adding the average forecast for each item. The aggregate standard deviation was
calculated by squaring the standard deviation for each
item (this is the variance), summing the variance for each
item, and then taking the square root of this sum. This
assumes that the demand for each school is independent,
meaning that the demand for Ohio State is totally unrelated to the demand at Michigan and the other schools.
You will allocate your aggregate order to the individual schools based on their expected percentage of total
demand. You discussed your analysis with Rhonda and
Steve and they are OK with your analysis. They would
like to see what the order quantities would be if each
school was considered individually.
You have a spreadsheet set up with all the data from
the exhibits called Big10Sweater.xls and you are ready to
do some calculations.
Chapter 20
557
Questions
1. You are curious as to how much Rhonda and Steve
made in their business last year. You do not have all
the data, but you know that most of their expenses
relate to buying the sweaters and having them monogrammed. You know they paid themselves $50,000
each and you know the rent, utilities, insurance, and a
benefit package for the business was about $20,000.
About how much do you think they made “before
taxes” last year? If they must make their payment to
the venture capital firm, and then pay 50 percent in
taxes, what was their increase in cash last year?
2. What was your reasoning behind using the aggregate demand forecast when determining the size of
your order rather than the individual school forecasts? Should you rethink this or is there a sound
basis for doing it this way?
3. How many sweaters should you order this year?
Break down your order by individual school. Document your calculations in your spreadsheet. Calculate this based on the aggregate forecast and also
the forecast by individual school.
4. What do you think they could make this year? They
are paying you $40,000 and you expect your benefit package addition would be about $1,000 per
year. Assume that they order based on the aggregate forecast.
5. How should the business be developed in the
future? Be specific and consider changes related to
your supplier, the monogramming subcontractor,
target customers, and products.
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. The model most appropriate for making a one-time
purchase of an item.
2. The model most appropriate when inventory is
replenished only in fixed intervals of time—for
example, on the first Monday of each month.
3. The model most appropriate when a fixed amount
must be purchased each time an order is placed.
4. Based on an EOQ-type ordering criterion, what cost
must be taken to zero if the desire is to have an order
quantity of a single unit?
5. Term used to describe demand that can be accurately
calculated to meet the need of a production schedule,
for example.
6. Term used to describe demand that is uncertain and
needs to be forecast.
7. We are ordering T-shirts for the spring party and are
selling them for twice what we paid for them. We
expect to sell 100 shirts and the standard deviation
associated with our forecast is 10 shirts. How many
shirts should we order?
8. We have an item that we stock in our store that has
fairly steady demand. Our supplier insists that we
buy 1,200 units at a time. The lead time is very short
on the item because the supplier is only a few blocks
away and we can pick up another 1,200 units when
we run out. How many units do you expect to have in
inventory, on average?
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Section 4
Supply and Demand Planning and Control
9. For the item described in question 8, if we expect to
sell approximately 15,600 units next year, how many
trips will we need to make to the supplier over the
year?
10. If we decide to carry 10 units of safety stock for the
item described in questions 8 and 9, and we implemented this by going to our supplier when we had
10 units left, how much inventory would you expect
to have, on average, now?
11. We are being evaluated based on the percentage of
total demand met in a year (not the probability of
stocking out as used in the chapter). Consider an
item that we are managing using a fixed–order quantity model with safety stock. We decide to double the
order quantity but leave the reorder point the same.
Would you expect the percent of total demand met
next year to go up or down? Why?
12. Consider an item for which we have 120 units currently in inventory. The average demand for the item
is 60 units per week. The lead time for the item is
exactly 2 weeks and we carry 16 units for safety
stock. What is the probability of running out of the
item if we order right now?
13. If we take advantage of a quantity discount, would
you expect your average inventory to go up or down?
Assume that the probability of stocking out criterion
stays the same.
14. This is an inventory auditing technique where inventory levels are checked more frequently than one
time a year.
Answers to Practice Exam 1. Single-period model 2. Fixed–time period model 3. Fixed–order quantity model 4. Setup or ordering cost 5. Dependent demand 6. Independent demand 7. 100 shirts 8. 600 units 9. 13 trips 10. 610 units 11. Go up (we are taking fewer chances of running out)
12. 50 percent 13. Will probably go up if the probability of stocking out stays the same 14. Cycle counting​​
Footnotes
1. P is actually a cumulative probability because the sale of the nth unit depends not only on exactly n being demanded but also on
the demand for any number greater than n.
2. As previously discussed, the standard deviation of a sum of independent variables equals the square root of the sum of the
variances.
3. The Pareto principle is also widely applied in quality problems through the use of Pareto charts. (See Chapter 12.)
Material
Requirements
Planning
21
Learning Objectives
LO 21–1
LO 21–2
LO 21–3
LO 21–4
Explain what material requirements planning (MRP) is.
Understand how the MRP system is structured.
Analyze an MRP problem.
Evaluate and compare MRP lot-sizing techniques.
INSI D E THE IPAD
So what does it cost for Apple Computer to build an iPad?
A good estimate can be made by taking one apart and evaluating the
cost of each component. There are many analysts who look at this each
time a new model iPad is introduced. Looking at many of these reports,
an estimate of the major costs for an iPad 3 with 64GB of memory is the
following:
Memory $80
Touchscreen and display $130
Processor $23
Cameras $12
Wi-Fi and sensors $15
Battery and power management $42
Other items $50
Box and charger $6
Manufacturing cost $10
So, for a total cost of about $368, Apple can build an iPad that it sells
for about $700. Of course, this does not include the cost to transport the
iPad and other support costs, but a profit of $332 is not bad.
© Aleksey Boldin/123RF
559
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UNDER STANDING MAT ERIAL REQUIREMENTS PLANNING
LO 21–1
Explain what material
requirements planning
(MRP) is.
Material requirements
planning (MRP)
The logic for determining
the number of parts,
components, and materials
needed to produce a
product.
Our emphasis in this chapter is on material requirements planning (MRP), which is the key
piece of logic that ties the production functions together from a material planning and control
view. MRP has been installed almost universally in manufacturing firms, even those considered small companies. The reason is that MRP is a logical, easily understandable approach
to the problem of determining the number of parts, components, and materials needed to
produce each end item. MRP also provides the schedule specifying when each of these items
should be ordered or produced.
MRP is based on dependent demand. Dependent demand is caused by the demand for
a higher-level item. Tires, wheels, and engines are dependent demand items based on the
demand for automobiles, for example.
Determining the number of dependent demand items needed is essentially a straightforward multiplication process. If one Part A takes five parts of B to make it, then five parts of
A require 25 parts of B. The basic difference in independent demand, covered in Chapter 20,
and dependent demand covered in this chapter, is as follows: If Part A is sold outside the firm,
the amount of Part A that we sell is uncertain. We need to create a forecast using past data
or do something like a market analysis. Part A is an independent item. However, Part B is a
dependent part and its use depends on Part A. The number of B needed is simply the number
of A times five. As a result of this type of multiplication, the requirements of other dependent
demand items tend to become more and more lumpy as we go farther down into the product creation sequence. Lumpiness means that the requirements tend to bunch or lump rather
than having an even dispersal. This is also caused by the way manufacturing is done. When
manufacturing occurs in lots (or batches), items needed to produce the lot are withdrawn from
inventory in quantities (perhaps all at once) rather than one at a time.
W he r e MRP C an Be Used
MRP is most valuable in industries where a number of products are made in batches using
the same productive equipment. The list in Exhibit 21.1 includes examples of different industry types and the expected benefit from MRP. As you can see in the exhibit, MRP is most
valuable to companies involved in assembly operations and least valuable to those in maketo-order fabrication. One more point to note: MRP does not work well in companies that produce a low number of units annually. Especially for companies producing complex, expensive
products requiring advanced research and design, experience has shown that lead times tend
to be too long and too uncertain, and the product configuration too complex. Such companies
need the control features that network scheduling techniques offer. These project management
methods are covered in Chapter 4.
An employee performs
the final quality
control check for the
make-to-stock company
making automobile tires.
© vario images GmbH &
Co.KG/Alamy
Material Requirements Planning
ex hibit 21.1
Chapter 21
Industry Applications and Expected Benefits of MRP
Expected
Benefits
Industry Type
Examples
Assemble-to-stock
Combines multiple component parts into a finished product,
which is then stocked in inventory to satisfy customer demand.
Examples: watches, tools, appliances.
High
Make-to-stock
Items are manufactured by machine rather than assembled
from parts. These are standard stock items carried in anticipation of customer demand. Examples: piston rings, electrical
switches.
Medium
Assemble-to-order
A final assembly is made from standard options that the customer chooses. Examples: trucks, generators, motors.
High
Make-to-order
Items are manufactured by machine to customer order. These
are generally industrial orders. Examples: bearings, gears,
fasteners.
Low
Engineer-to-order
Items are fabricated or assembled completely to customer
specification. Examples: turbine generators, heavy machine
tools.
High
Process
Includes industries such as foundries, rubber and plastics,
specialty paper, chemicals, paint, drug, food processors.
Medium
M as t e r Pr oduction S che du lin g
Generally, the master production schedule deals with end items (typically finished goods
items sold to customers) and is a major input to the MRP process. If the end item is quite
large or quite expensive, however, the master schedule may schedule major subassemblies or
components instead.
All production systems have limited capacity and limited resources. This presents a challenging job for the master scheduler. Although the aggregate plan provides the general range
of operation, the master scheduler must specify exactly what is to be produced. These decisions are made while responding to pressures from various functional areas such as the sales
department (meet the customer’s promised due date), finance (minimize inventory), management (maximize productivity and customer service, minimize resource needs), and manufacturing (have level schedules and minimize setup time).
To determine an acceptable, feasible schedule to be released to the shop, trial master production schedules are run through the MRP program, which is described in the next section.
The resulting planned order releases (the detailed production schedules) are checked to make
sure that resources are available and that the completion times are reasonable. What appears
to be a feasible master schedule may turn out to require excessive resources once the required
materials, parts, and components from lower levels are determined. If this does happen (the
usual case), the master production schedule is then modified with these limitations and
the MRP program is run again. To ensure good master scheduling, the master scheduler (the
human being) must
∙
∙
∙
∙
∙
∙
Include all demands from product sales, warehouse replenishment, spares, and interplant requirements.
Never lose sight of the aggregate plan.
Be involved with customer order promising.
Be visible to all levels of management.
Objectively trade off manufacturing, marketing, and engineering conflicts.
Identify and communicate all problems.
The upper portion of Exhibit 21.2 shows an aggregate plan for the total number of mattresses planned per month, without regard for mattress type. The lower portion shows a master production schedule specifying the exact type of mattress and the quantity planned for
561
562
Section 4
Supply and Demand Planning and Control
exhibit 21.2
The Aggregate Plan and the Master Production Schedule for
Mattresses
Aggregate Production
Plan for Mattresses
Month
Mattress production
Master Production
Schedule for Mattress
Models
1
Model 327
Model 538
Model 749
Master production
schedule (MPS)
A time-phased plan
specifying how many of
each end item the firm
plans to build and when.
Available to promise
A feature of MRP systems
that identifies the
difference between the
number of units currently
included in the master
schedule and the actual
(firm) customer orders.
1
900
2
2
950
3
200
Week
4
5
400
100
100
100
150
6
7
200
100
100
200
8
200
production by week. In month 1, for example, a total of 900 mattresses are scheduled: 600
model 327s, 200 model 538s, and 100 model 749s. The next level down (not shown) would be
the MRP program that develops detailed schedules showing when cotton batting, springs, and
hardwood are needed to make the mattresses.
To again summarize the planning sequence, the aggregate operations plan, discussed in
Chapter 19, specifies product groups. It does not specify exact items. The next level down in
the planning process is the master production schedule. The master production schedule
(MPS) is the time-phased plan specifying how many of each end item the firm plans to build
and when. For example, the aggregate plan for a furniture company may specify the total volume of mattresses it plans to produce over the next month or next quarter. The MPS goes the
next step down and identifies the exact size of the mattresses and their qualities and styles. All
of the mattresses sold by the company would be specified by the MPS. The MPS also states
period by period (usually weekly) how many and when each of these mattress types is needed.
Still further down the disaggregation process is the MRP program, which calculates and
schedules all raw materials, parts, and supplies needed to make the mattress specified by the
MPS.
T i m e F e n c e s The question of flexibility within a master production schedule depends
on several factors: production lead time, commitment of parts and components to a specific
end item, relationship between the customer and vendor, amount of excess capacity, and the
reluctance or willingness of management to make changes.
The purpose of time fences is to maintain a reasonably controlled flow through the production system. Unless some operating rules are established and adhered to, the system could be
chaotic and filled with overdue orders and constant expediting.
Exhibit 21.3 shows an example of a master production schedule time fence. Management
defines time fences as periods of time having some specified level of opportunity for the customer to make changes. (The customer may be the firm’s own marketing department, which
may be considering product promotions, broadening variety, or the like.) Note in the exhibit
that for the next eight weeks, this particular master schedule is frozen. Each firm has its own
time fences and operating rules. Under these rules, frozen could be defined as anything from
absolutely no changes in one company to only the most minor of changes in another. Slushy
may allow changes in specific products within a product group so long as parts are available.
Liquid may allow almost any variations in products, with the provisions that capacity remains
about the same and that there are no long lead time items involved.
Some firms use a feature known as available to promise for items that are master scheduled. This feature identifies the difference between the number of units currently included in
the master schedule and firm customer orders. For example, assume the master schedule indicates that 100 units of Model 538 mattress are going to be made during week seven. If firm
Material Requirements Planning
ex hibit 21.3
Chapter 21
563
Master Production Schedule Time Fences
Frozen
Slushy
Liquid
Capacity
Forecast and available
capacity
Firm customer orders
8
Weeks
15
26
customer orders now only indicate that 65 of those mattresses have actually been sold, the
sales group has another 35 mattresses “available to promise” for delivery during that week.
This can be a powerful tool for coordinating sales and production activities.
MATER IAL REQUIREMENTS PLANNING
SYSTEM STRUCTURE
The material requirements planning portion of manufacturing activities most closely interacts
with the master schedule, bill-of-materials file, inventory records file, and output reports as
shown in Exhibit 21.4.
Each facet of Exhibit 21.4 is detailed in the following sections, but essentially the MRP
system works as follows: The master production schedule states the number of items to be
produced during specific time periods. A bill-of-materials file identifies the specific materials
used to make each item and the correct quantities of each. The inventory records file contains
data such as the number of units on hand and on order. These three sources—master production schedule, bill-of-materials file, and inventory records file—become the data sources for
the material requirements program, which expands the production schedule into a detailed
order scheduling plan for the entire production sequence.
LO 21–2
Understand how the MRP
system is structured.
D e ma n d for Pr oducts
Product demand for end items comes primarily from two main sources. The first is known
customers who have placed specific orders, such as those generated by sales personnel, or
from interdepartment transactions. These orders usually carry promised delivery dates. There
is no forecasting involved in these orders—simply add them up. The second source is the
aggregate production plan (described in Chapter 19). The aggregate plan reflects the firm’s
strategy for meeting demand in the future. The strategy is implemented through the detailed
master production schedule.
In addition to the demand for end products, customers also order specific parts and components either as spares or for service and repair. These demands are not usually part of the
master production schedule; instead, they are fed directly into the material requirements planning program at the appropriate levels. That is, they are added in as a gross requirement for
that part or component.
B i l l- of- M a te r ia ls
The bill-of-materials (BOM) file contains the complete product description, listing the materials, parts, and components; the quantity of each item; and also the sequence in which the
product is created. This BOM file is one of the three main inputs to the MRP program. (The
other two are the master schedule and the inventory records file.)
Bill-of-Materials (BOM)
The complete product
description, listing the
materials, parts, and
components; the quantity
of each item; and also the
sequence in which the
product is created.
564
Section 4
Supply and Demand Planning and Control
exhibit 21.4
Overall View of the Inputs to a Standard Material Requirements
Planning Program and the Reports Generated by the Program
Forecasts
of demand
from
customers
Aggregate
production
plan
Firm orders
from
customers
Engineering
design
changes
Master
production
schedule
(MPS)
Inventory
transactions
Bill-ofmaterials
file
Material
planning
(MRP
computer
program)
Inventory
records
file
Production
activity
reports
Primary reports
Secondary reports
Planned order releases for
inventory and production
control
Exceptions reports
Planning reports
Reports for performance control
The BOM file is often called the product structure file or product tree because it shows
how a product is put together. It contains the information to identify each item and the quantity used per unit of the item of which it is a part. To illustrate this, consider Product A shown
in Exhibit 21.5A. Product A is made of two units of Part B and three units of Part C. Part B is
made of one unit of Part D and four units of Part E. Part C is made of two units of Part F, five
units of Part G, and four units of Part H.
Bill-of-materials files often list parts using an indented structure. This clearly identifies
each item and the manner in which it is assembled because each indentation signifies the
components of the item. A comparison of the indented parts in Exhibit 21.5B with the item
structure in Exhibit 21.5A shows the ease of relating the two displays. From a computer standpoint, however, storing items in indented parts lists is very inefficient. To compute the amount
of each item needed at the lower levels, each item would need to be expanded (“exploded”)
and summed. A more efficient procedure is to store parts data in simple single-level lists. That
is, each item and component is listed showing only its parent and the number of units needed
per unit of its parent. This avoids duplication because it includes each assembly only once.
Exhibit 21.5B shows both the indented parts list and the single-level parts list for Product A.
A modular bill-of-materials is the term for a buildable item that can be produced and
stocked as a subassembly. It is also a standard item with no options within the module. Many
end items that are large and expensive are better scheduled and controlled as modules (or
subassemblies). It is particularly advantageous to schedule subassembly modules when the
Material Requirements Planning
ex hibit 21.5
Chapter 21
A. Bill-of-Materials (Product Structure Tree) for Product A
A
B(2)
D(1)
C(3)
E(4)
F(2)
G(5)
H(4)
B. Parts List in an Indented Format and in a Single-Level List
Indented Parts List
Single-Level Parts List
A
A
B(2)
C(3)
B(2)
D(1)
E(4)
B
F(2)
G(5)
H(4)
C
D(1)
E(4)
C(3)
F(2)
G(5)
H(4)
same subassemblies appear in different end items. For example, a manufacturer of cranes can
combine booms, transmissions, and engines in a variety of ways to meet a customer’s needs.
Using a modular bill-of-materials simplifies the scheduling and control and also makes it
easier to forecast the use of different modules. Another benefit in using modular bills is that
if the same item is used in a number of products, then the total inventory investment can be
minimized.
A super bill-of-materials includes items with fractional options. (A super bill can specify,
for example, 0.3 of a part. What that means is that 30 percent of the units produced contain
that part and 70 percent do not.) Modular and super bills-of-materials are often referred to as
planning bills-of-materials because they simplify the planning process.
L o w - L e v e l C o d i n g If all identical parts occur at the same level for each end product,
the total number of parts and materials needed for a product can be computed easily. Consider
Product L shown in Exhibit 21.6A. Notice that Item N, for example, occurs both as an input
to L and as an input to M. Item N, therefore, needs to be lowered to level 2 (Exhibit 21.6B) to
bring all Ns to the same level. If all identical items are placed at the same level, it becomes a
simple matter for the computer to scan across each level and summarize the number of units
of each item required.
I n ve n t or y Re cor ds
The inventory records file can be quite lengthy. Exhibit 21.7 shows the variety of information contained in the inventory records. The MRP program accesses the status segment of the
record according to specific time periods (called time buckets in MRP slang). These records
are accessed as needed during the program run.
As we will see, the MRP program performs its analysis from the top of the product structure downward, calculating requirements level by level. There are times, however, when it is
desirable to identify the parent item that caused the material requirement. For example, we
565
566
Supply and Demand Planning and Control
Section 4
Product L Hierarchy in (A) Expanded to the Lowest Level of Each Item in (B)
exhibit 21.6
A. BOM for Product L
Level
L
0
L
M
1
N
P
2
3
B. Low-Level Coded BOM
R
4
N
S
Q
Q
R
M
R
P
S
N
R
Q
S
S
exhibit 21.7
N
R
Q
R
S
S
The Inventory Status Record for an Item in Inventory
Part no.
Item master
data segment
Description
Order quantity
Setup
Scrap allowance
Cutting data
Allocated
Inventory
status
segment
SUBSIDIARY
DATA
Lead time
Gross
requirements
Scheduled
receipts
Projected
available balance
Planned order
releases
Order details
Pending action
Counters
Keeping track
Control
balance
Cycle
Std. cost
Safety stock
Last year's usage
Pointers
Period
1 2 3 4 5 6 7 8
Class
Etc.
Totals
may want to know what subassemblies are generating the requirement for a part that we order
from a supplier. The MRP program allows the creation of a peg record file either separately
or as part of the inventory record file. Pegging requirements allows us to retrace a material
requirement upward in the product structure through each level, identifying each parent item
that created the demand.
KEY IDEA
MRP programs are
integrated into ERP
systems offered by
companies such as SAP
and Oracle.
I n v e n t o r y T r a n s a c t i o n s F i l e The inventory status file is kept up-to-date by
posting inventory transactions as they occur. These changes occur because of stock receipts
and disbursements, scrap losses, wrong parts, canceled orders, and so forth.
M RP Com p u t er Pro gram
The material requirements planning program operates using information from the inventory
records, the master schedule, and the bill-of-materials. The process of calculating the exact
requirements for each item managed by the system is often referred to as the “explosion” process. Working from the top level downward in the bill-of-materials, requirements from parent
Material Requirements Planning
Chapter 21
567
items are used to calculate the requirements for component items. Consideration is taken of
current on-hand balances and orders that are scheduled for receipt in the future.
The following is a general description of the MRP explosion process:
1.
2.
3.
4.
5.
6.
7.
8.
The requirements for level 0 items, typically referred to as end items, are retrieved
from the master schedule. These requirements are referred to as gross requirements
by the MRP program. Typically, the gross requirements are scheduled in weekly time
buckets.
Next, the program uses the current on-hand balance together with the schedule
of orders that will be received in the future to calculate the net requirements. Net
requirements are the amounts needed week by week in the future over and above
what is currently on hand or committed to through an order already released and
scheduled.
Using net requirements, the program calculates when orders should be received to
meet these requirements. This can be a simple process of just scheduling orders to
arrive according to the exact net requirements or a more complicated process where
requirements are combined for multiple periods. This schedule of when orders should
arrive is referred to as planned-order receipts.
Because there is typically a lead time associated with each order, the next step is
to find a schedule for when orders are actually released. Offsetting the plannedorder receipts by the required lead time does this. This schedule is referred to as the
planned-order release.
After these four steps have been completed for all the level zero items, the program
moves to level 1 items.
The gross requirements for each level 1 item are calculated from the planned-order
release schedule for the parents of each level 1 item. Any additional independent
demand also needs to be included in the gross requirements.
After the gross requirements have been determined, net requirements, planned-order
receipts, and planned-order releases are calculated as described in steps 2 to 4.
This process is then repeated for each level in the bill-of-materials.
The process of doing these calculations is much simpler than the description, as you will
see in the example that follows. Typically, the explosion calculations are performed each week
or whenever changes have been made to the master schedule. Some MRP programs have the
option of generating immediate schedules, called net change schedules. Net change systems
are “activity” driven and requirements and schedules are updated whenever a transaction is
processed that has an impact on the item. Net change enables the system to reflect in real time
the exact status of each item managed by the system.
Net change systems
MRP systems that calculate
the impact of a change
in the MRP data (the
inventory status, BOM,
or master schedule)
immediately.
AN EX AMPLE USING MRP
Ampere, Inc., produces a line of electric meters installed in residential buildings by electric
utility companies to measure power consumption. Meters used on single-family homes are
of two basic types for different voltage and amperage ranges. In addition to complete meters,
some subassemblies are sold separately for repair or for changeovers to a different voltage or
power load. The problem for the MRP system is to determine a production schedule to identify each item, the period when it is needed, and the appropriate quantities. The schedule is
then checked for feasibility, and the schedule is modified if necessary.
For e ca s t ing De m a nd
Demand for the meters and components originates from two sources: regular customers that
place firm orders in advance based on the needs of their projects and other, typically smaller,
customers that buy these items as needed. The smaller customer requirements were forecast
LO 21–3
Analyze an MRP problem.
568
Supply and Demand Planning and Control
Section 4
Future Requirements for Meters A and B and Subassembly D
Stemming from Specific Customer Orders and from Forecasts
exhibit 21.8
Meter A
Meter B
Subassembly D
Month
Known
Forecast
Known
Forecast
Known
Forecast
3
1,000
250
410
60
200
70
4
600
250
300
60
180
70
5
300
250
500
60
250
70
using one of the usual techniques described in Chapter 18 and past demand data. Exhibit 21.8
shows the requirements for meters A and B and subassembly D for a three-month period
(Months 3 through 5). There are some “other parts” used to make the meters. In order to keep
our example manageable, we are not including them in this example.
D e ve lop in g a Mast er Pro d u ctio n Sch ed u le
For the meter and component requirements specified in Exhibit 21.8, assume that the
­quantities to satisfy the known and random demands must be available during the first week
of the month. This assumption is reasonable because management (in our example) prefers
to produce meters in a single batch each month rather than a number of batches throughout
the month.
Exhibit 21.9 shows the trial master schedule that we use under these conditions, with
demand for Months 3, 4, and 5 listed in the first week of each month, or as Weeks 9, 13, and
17. For brevity, we will work with demand through Week 9. The schedule we develop should
be examined for resource availability, capacity availability, and so on, and then revised and
run again. We will stop with our example at the end of this one schedule, however.
B ill- of- Ma t e rials (Pro d u ct Stru ctu re)
The product structure for meters A and B is shown in Exhibit 21.10A in the typical way using
low-level coding, in which each item is placed at the lowest level at which it appears in the
structure hierarchy. Meters A and B consist of a common subassembly C and some parts that
include part D. To keep things simple, we will focus on only one of the parts, part D, which
is a transformer.
From the product structure, notice that part D (the transformer) is used in subassembly C
(which is used in both meters A and B). In the case of meter A, an additional part D (transformer) is needed. The “2” in parentheses next to D when used to make a C indicates that two
Ds are required for every C that is made. The product structure, as well as the indented parts
list in Exhibit 21.10B, indicates how the meters are actually made. First, subassembly C is
made, and potentially these are carried in inventory. In a final assembly process, meters A and
B are put together, and in the case of meter A an additional part D is used.
exhibit 21.9
A Master Schedule to Satisfy Demand Requirements as Specified in
Exhibit 21.8
Week
9
10
11
12
13
14
15
16
17
Meter A
1,250
850
550
Meter B
470
360
560
Subassembly D
270
250
320
Material Requirements Planning
ex hibit 21.10
569
Chapter 21
A. Product Structure for Meters A and B
Level 0
Meter A
Meter B
A
B
Level 1
Level 2
D(1)
C(1)
C(1)
D(2)
D(2)
B. Indented Parts List for Meter A and Meter B, with the Required Number of Items
per Unit of Parent Listed in Parentheses
Meter A
Meter B
A
B
D(1)
C(1)
C(1)
D(2)
D(2)
Exhibit 12.10B shows the subassemblies and parts that make up the meters and shows the
numbers of units required per unit of parent in parentheses.
I n ve n t or y Re cor ds
The inventory records data would be similar to those shown in Exhibit 21.7. As shown earlier in the chapter, additional data such as vendor identity, cost, and lead time also would be
included in these data. For this example, the pertinent data include the on-hand inventory at
the start of the program run, safety stock requirements, and the current status of orders that
have already been released (see Exhibit 21.11). Safety stock is a minimum amount of inventory that we always want to keep on hand for an item. For example, for subassembly C, we
never want the inventory to get below 5 units. We also see that we have an order for 10 units of
meter B that is scheduled for receipt at the beginning of Week 5. Another order for 100 units
of part D (the transformer) is scheduled to arrive at the beginning of Week 4.
Pe r for m ing the M RP Calcu la t io n s
Conditions are now set to perform the MRP calculations: End-item requirements have been
presented in the master production schedule, while the status of inventory and the order lead
times are available, and we also have the pertinent product structure data. The MRP calculations (often referred to as an explosion) are done level by level, in conjunction with the inventory data and data from the master schedule.
ex hibit 21.11
Number of Units On Hand and Lead Time Data that Would Appear on
the Inventory Record File
Item
On-Hand Inventory
Lead Time (Weeks)
Safety Stock
A
50
2
0
B
60
2
0
C
40
1
5
D
200
1
20
On Order
10 (Week 5)
100 (Week 4)
570
Section 4
exhibit 21.12
Supply and Demand Planning and Control
Material Requirements Planning Schedule for Meters A and B, and Subassemblies C and D
Week
4
Item
A
LT = 2 weeks
On hand = 50
Safety stock = 0
Order qty = lot-for-lot
B
LT = 2 weeks
On hand = 60
Safety stock = 0
Order qty = lot-for-lot
C
LT = 1 week
On hand = 40
Safety stock = 5
Order qty = 2,000
D
LT = 1 week
On hand = 200
Safety stock = 20
Order qty = 5,000
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned order receipts
Planned order releases
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned order receipts
Planned order releases
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned order receipts
Planned order releases
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned order receipts
Planned order releases
5
6
7
8
9
1,250
50
50
50
50
50
1,200
60
10
70
0
1,200
1,200
470
70
70
70
0
400
400
435
435
400
400+
1,200
35
35
35
2,000
100
280
280
5,000
435
1,565
2,000
4,000
1,200
1,280
3,720
5,000
80
270
80
5,000
4,810
190
5,000
Exhibit 21.12 shows the details of these calculations. The following analysis explains the
logic in detail. We will limit our analysis to the problem of meeting the gross requirements for
1,250 units of meter A, 470 units of meter B, and 270 units of transformer D, all in Week 9.
An MRP record is kept for each item managed by the system. The record contains gross
requirements, scheduled receipts, projected available balance, net requirements, planned
order receipts, and planned order releases data. Gross requirements are the total amount
required for a particular item. These requirements can be from external customer demand and
also from demand calculated due to manufacturing requirements. Scheduled receipts represent orders that have already been released and that are scheduled to arrive as of the beginning of the period. Once the paperwork on an order has been released, what was a “planned”
order prior to that event now becomes a scheduled receipt. Projected available balance is the
amount of inventory expected as of the end of a period. This can be calculated as follows:
Projected Projected
Planned
Gross
Scheduled
​​available​
​
​= available​
​
​​− ​requirements
​
​+ ​receipts ​+ order
​
​ ​​​
t
t
receiptst
balancet
balancet−1
One thing that needs to be considered is the initial projected available balance. In the case
where safety stock is needed, the on-hand balance needs to be reduced by the safety stock. So
projected available balance in period zero is on hand minus the safety stock.
A net requirement is the amount needed when the projected available balance plus the
scheduled receipts in a period are not sufficient to cover the gross requirement. The planned
order receipt is the amount of an order that is required to meet a net requirement in the period.
Finally, the planned order release is the planned order receipt offset by the lead time.
Material Requirements Planning
Chapter 21
EXAMPLE 21.1: MRP Explosion Calculations
Juno Lighting makes special lights that are popular in new homes. Juno expects demand for
two popular lights to be the following over the next eight weeks.
Week
1
2
3
4
5
6
7
8
VH1-234
34
37
41
45
48
48
48
48
VH2-100
104
134
144
155
134
140
141
145
A key component in both lights is a socket that the bulb is screwed into in the base fixture.
Each light has one of these sockets. Given the following information, plan the production of
the lights and purchases of the socket.
VH1-234
VH2-100
Light Socket
On hand
85
358
425
Q
200 (the production lot size)
400 (the production lot size)
500 (purchase quantity)
Lead time
1 week
1 week
3 weeks
Safety stock
0 units
0 units
20 units
SOLUTION
Week
Item
VH1-234
Q = 200
LT = 1
OH = 85
SS = 0
VH2-100
Q = 400
LT = 1
OH = 358
SS = 0
Socket
Q = 500
LT = 3
OH = 425
SS = 20
1
2
3
4
5
6
7
8
Gross requirement
Scheduled receipts
Projected available
balance
Net requirements
Planned order receipts
Planned order releases
34
37
41
45
48
48
48
48
51
14
173
27
200
128
80
32
184
16
200
136
Gross requirement
Scheduled receipts
Projected available
balance
Net requirements
Planned order receipts
Planned order releases
104
134
144
155
134
140
141
145
254
120
376
24
400
221
87
347
53
400
206
61
205
205
Gross requirement
Scheduled receipts
Projected available
balance
Net requirements
Planned order receipts
Planned order releases
200
200
400
400
600
400
200
405
95
500
205
500
905
305
305
305
500
The best way to proceed is to work period by period by focusing on the projected available balance calculation. Whenever the available balance goes below zero, a net requirement is generated. When this happens, plan an order receipt to meet the requirement. For example, for VH1
we start with 85 units in inventory and need 34 to meet Week 1 production requirements. This
brings our available balance at the end of Week 1 to 51 units. Another 37 units are used during
Week 2, dropping inventory to 14. In Week 3, our projected balance drops to 0 and we have a
net requirement of 27 units that needs to be covered with an order scheduled to be received in
Week 3. Because the lead time is one week, this order needs to be released in Week 2. Week 4
projected available balance is 128, calculated by taking the 200 units received in Week 3 and
subtracting the Week 3 net requirement of 27 units and the 45 units needed for Week 4.
Because sockets are used in both VH1 and VH2, the gross requirements come from the
planned order releases for these items: 600 are needed in Week 2 (200 for VH1s and 400 for
VH2s), 400 in Week 5, and 200 in Week 6. Projected available balance is beginning inventory
of 425 plus the scheduled receipts of 500 units minus the 20 units of safety stock.
571
572
Section 4
Supply and Demand Planning and Control
Beginning with meter A, the projected available balance is 50 units and there are no net
requirements until Week 9. In Week 9, an additional 1,200 units are needed to cover the
demand of 1,250 generated from the order scheduled through the master schedule. The order
quantity is designated “lot-for-lot,” which means that we can order the exact quantity needed
to meet net requirements. An order, therefore, is planned for receipt of 1,200 units for the
beginning of Week 9. Because the lead time is two weeks, this order must be released at the
beginning of Week 7.
Meter B is similar to A, although an order for 10 units is scheduled for receipt in period
5. We project that 70 units will be available at the end of Week 5. There is a net requirement for 400 additional units to meet the gross requirement of 470 units in Week 9. This
requirement is met with an order for 400 units that must be released at the beginning of
Week 7.
Item C is the subassembly used in both meters A and B. We only need additional Cs
when either A or B is being made. Our analysis of A indicates that an order for 1,200 will
be released in Week 7. An order for 400 Bs also will be released in Week 7, so total demand
for C is 1,600 units in Week 7. The projected available balance is the 40 units on hand minus
the safety stock of 5 units that we have specified, or 35 units. In Week 7, the net requirement
is 1,565 units. The order policy for C indicates an order quantity of 2,000 units, so an order
receipt for 2,000 is planned for Week 7. This order needs to be released in Week 6 due to the
one-week lead time. Assuming this order is actually processed in the future, the projected
available balance is 435 units in Weeks 7, 8, and 9.
Item D, the transformer, has demand from three different sources. The demand in Week
6 is due to the requirement to put Ds into subassembly C. In this case, two Ds are needed
for every C, or 4,000 units (the product structure indicates this two-to-one relationship). In
the seventh week, 1,200 Ds are needed for the order for 1,200 As that are scheduled to be
released in Week 7. Another 270 units are needed in Week 9 to meet the independent demand
scheduled through the master schedule. Projected available balance at the end of Week 4 is
280 units (200 on hand plus the scheduled receipt of 100 units minus the safety stock of 20
units) and 280 units in Week 5. There is a net requirement for an additional 3,720 units in
Week 6, so we plan to receive an order for 5,000 units (the order quantity). This results in
a projected balance of 1,280 in Week 6 and 80 in Week 7 because 1,200 are used to meet
demand. Eighty units are projected to be available in Week 8. Due to the demand for 270 in
Week 9, a net requirement of 190 units in Week 9 results in planning the receipt of an additional 5,000-unit order in Week 9.
LOT SI ZI NG IN MRP SYSTEMS
LO 21–4
Evaluate and compare
MRP lot-sizing techniques.
The determination of lot sizes in an MRP system is a complicated and difficult problem. Lot
sizes are the part quantities issued in the planned order receipt and planned order release sections of an MRP schedule. For parts produced in-house, lot sizes are the production quantities
of batch sizes. For purchased parts, these are the quantities ordered from the supplier. Lot
sizes generally meet part requirements for one or more periods.
Most lot-sizing techniques deal with how to balance the setup or order costs and holding
costs associated with meeting the net requirements generated by the MRP planning process.
Many MRP systems have options for computing lot sizes based on some of the more commonly used techniques. The use of lot-sizing techniques increases the complexity of running MRP schedules in a plant. In an attempt to save setup costs, the inventory generated
with the larger lot sizes needs to be stored, making the logistics in the plant much more
complicated.
Next we explain four lot-sizing techniques using a common example. The lot-sizing techniques presented are lot-for-lot (L4L), economic order quantity (EOQ), least total cost (LTC),
and least unit cost (LUC).
Material Requirements Planning
Chapter 21
573
Consider the following MRP lot-sizing problem; the net requirements are shown for eight
scheduling weeks:
Cost per item
$10.00
Order or setup cost
$47.00
Inventory carrying cost/week
0.5%
Weekly net requirements:
1
2
3
4
5
6
7
8
50
60
70
60
95
75
60
55
Lot - for - Lot
Lot-for-lot (L4L) is the most common technique. It
∙
∙
Sets planned orders to exactly match the net requirements.
Produces exactly what is needed each week with no inventory carried over into future
periods.
Minimizes carrying cost.
Does not take into account setup costs or capacity limitations.
∙
∙
Exhibit 21.13 shows the lot-for-lot calculations. The net requirements are given in column 2.
Because the logic of lot-for-lot says the production quantity (column 3) will exactly match the
required quantity (column 2), there will be no inventory left at the end (column 4). Without any
inventory to carry over into the next week, there is zero holding cost (column 5). However, lotfor-lot requires a setup cost each week (column 6). Incidentally, there is a setup cost each week
because this is a workcenter where a variety of items are worked on each week. This is not a
case where the workcenter is committed to one product and sits idle when it is not working on
that product (in which case only one setup would result). Lot-for-lot causes high setup costs.
E c o n om ic Or de r Qua ntit y
In Chapter 20, we discussed the EOQ model that explicitly balances setup and holding costs.
In an EOQ model, either fairly constant demand must exist or safety stock must be kept to
provide for demand variability. The EOQ model uses an estimate of total annual demand, the
setup or order cost, and the annual holding cost. EOQ was not designed for a system with
discrete time periods such as MRP. The lot-sizing techniques used for MRP assume that part
requirements are satisfied at the start of the period. Holding costs are then charged only to the
ending inventory for the period, not to the average inventory as in the case of the EOQ model.
EOQ assumes that parts are used continuously during the period. The lot sizes generated by
EOQ do not always cover the entire number of periods. For example, the EOQ might provide
Lot-for-Lot Run Size for an MRP Schedule
ex hibit 21.13
(1)
Week
(2)
Net Requirements
(3)
Production Quantity
(4)
Ending Inventory
(5)
Holding Cost
(6)
Setup Cost
(7)
Total Cost
1
50
50
0
$0.00
$47.00
$ 47.00
2
60
60
0
0.00
47.00
94.00
3
70
70
0
0.00
47.00
141.00
4
60
60
0
0.00
47.00
188.00
5
95
95
0
0.00
47.00
235.00
6
75
75
0
0.00
47.00
282.00
7
60
60
0
0.00
47.00
329.00
8
55
55
0
0.00
47.00
376.00
574
Supply and Demand Planning and Control
Section 4
the requirements for 4.6 periods. Using the same data as in the lot-for-lot example, the economic order quantity is calculated as follows:
Annual demand based on the 8 weeks = D = ___
​  525 ​× 52 = 3, 412.5 units
8
Annual holding cost = H = 0.5 % × $10 × 52 weeks = $2.60 per unit
​​
​
​​
​ ​
​Setup cost = S = $47​(​given​)​
____
____________
2​​(​3, 412.5​)​(​$47​)​
____________
EOQ= ​ ____
​2DS ​ = ​
​  ​ = 351 units
√
H
√
$2.60
Exhibit 21.14 shows the MRP schedule using an EOQ of 351 units. The EOQ lot size in Week
1 is enough to meet requirements for Weeks 1 through 5 and a portion of Week 6. Then, in
Week 6 another EOQ lot is planned to meet the requirements for Weeks 6 through 8. Notice
that the EOQ plan leaves some inventory at the end of Week 8 to carry forward into Week 9.
Le a s t Tot a l C o st
The least total cost method (LTC) is a dynamic lot-sizing technique that calculates the order
quantity by comparing the carrying cost and the setup (or ordering) costs for various lot sizes
and then selects the lot in which these are most nearly equal.
The top half of Exhibit 21.15 shows the least cost lot size results. The procedure to compute
least total cost lot sizes is to compare order costs and holding costs for various numbers of
weeks. For example, costs are compared for producing in Week 1 to cover the requirements for
Week 1; producing in Week 1 for Weeks 1 and 2; producing in Week 1 to cover Weeks 1, 2, and
3; and so on. The correct selection is the lot size where the ordering costs and holding costs are
approximately equal. In Exhibit 21.15, the best lot size is 335 because a $38 carrying cost and a
$47 ordering cost are closer than $56.75 and $47 ($9 versus $9.75). This lot size covers requirements for Weeks 1 through 5. Unlike EOQ, the lot size covers only whole numbers of periods.
Based on the Week 1 decision to place an order to cover five weeks, we are now located
in Week 6, and our problem is to determine how many weeks into the future we can provide
for from here. Exhibit 21.15 shows that holding and ordering costs are closest in the quantity that covers requirements for Weeks 6 through 8. Notice that the holding and ordering
costs here are far apart. This is because our example extends only to Week 8. If the planning
horizon were longer, the lot size planned for Week 6 would likely cover more weeks into the
future beyond Week 8. This brings up one of the limitations of both LTC and LUC (discussed
below). Both techniques are influenced by the length of the planning horizon. The bottom half
of Exhibit 21.15 shows the final run size and total cost.
Le a s t U nit C o st
The least unit cost method is a dynamic lot-sizing technique that adds ordering and inventory
carrying cost for each trial lot size and divides by the number of units in each lot size, picking
the lot size with the lowest unit cost. The top half of Exhibit 21.16 calculates the unit cost for
exhibit 21.14
Economic Order Quantity Run Size for an MRP Schedule
Week
Net Requirements
Production Quantity
Ending Inventory
Holding Cost
Setup Cost
Total Cost
1
2
3
4
5
6
7
8
50
60
70
60
95
75
60
55
351
0
0
0
0
351
0
0
301
241
171
111
16
292
232
177
$15.05
12.05
8.55
5.55
0.80
14.60
11.60
8.85
$47.00
0.00
0.00
0.00
0.00
47.00
0.00
0.00
$62.05
74.10
82.65
88.20
89.00
150.60
162.20
171.05
Material Requirements Planning
Least Total Cost Run Size for an MRP Schedule
exhibit 21.15
Weeks
575
Chapter 21
Quantity Ordered
Carrying Cost
Order Cost
Total Cost
1
50
$ 0.00
$47.00
$ 47.00
1–2
110
3.00
47.00
50.00
1–3
180
10.00
47.00
57.00
1–4
240
19.00
47.00
66.00
1–5
335
38.00
47.00
85.00 ← Least total cost
1–6
410
56.75
47.00
103.75
1–7
470
74.75
47.00
121.75
1–8
525
94.00
47.00
141.00
6
75
0.00
47.00
47.00
6–7
135
3.00
47.00
50.00
6–8
190
8.50
47.00
55.50 ← Least total cost
Week
Net Requirements
Production Quantity
Ending Inventory
1
50
335
285
$14.25
$47.00
$ 61.25
2
60
0
225
11.25
0.00
72.50
3
70
0
155
7.75
0.00
80.25
4
60
0
95
4.75
0.00
85.00
5
95
0
0
0.00
0.00
85.00
6
75
190
115
5.75
47.00
137.75
7
60
0
55
2.75
0.00
140.50
8
55
0
0
0.00
0.00
140.50
exhibit 21.16
Weeks
1st order
2nd order
Holding Cost
Setup Cost
Total Cost
Least Total Cost Run Size for an MRP Schedule
Quantity Ordered
Carrying Cost
Order Cost
Total Cost
Unit Cost
1
50
$ 0.00
$47.00
$ 47.00
$0.9400
1–2
110
3.00
47.00
50.00
0.4545
1–3
180
10.00
47.00
57.00
0.3167
1–4
240
19.00
47.00
66.00
0.2750
1–5
335
38.00
47.00
85.00
0.2537
1–6
410
56.75
47.00
103.75
0.2530 ← Least unit cost
1–7
470
74.75
47.00
121.75
0.2590
1–8
525
94.00
47.00
141.00
0.2686
?
60
0.00
47.00
47.00
0.7833
7–8
115
2.75
47.00
49.75
0.4326 ← Least unit cost
Week
Net Requirements
1
50
2
3
Production Quantity
1st order
2nd order
Ending Inventory
Holding Cost
Setup Cost
Total Cost
410
360
$18.00
$47.00
$ 65.00
60
0
300
15.00
0.00
80.00
70
0
230
11.50
0.00
91.50
4
60
0
170
8.50
0.00
100.00
5
95
0
75
3.75
0.00
103.75
6
75
0
0
0
0
103.75
7
60
115
55
2.75
47.00
153.50
8
55
0
0
0
0
$153.50
576
Section 4
Supply and Demand Planning and Control
ordering lots to meet the needs of Weeks 1 through 8. Note that the minimum occurred when
the quantity 410, ordered in Week 1, was sufficient to cover Weeks 1 through 6. The lot size
planned for Week 7 covers through the end of the planning horizon.
The least unit cost run size and total cost are shown in the bottom half of Exhibit 21.16.
Choos ing th e Best Lo t Size
Using the lot-for-lot method, the total cost for the eight weeks is $376; the EOQ total cost is
$171.05; the least total cost method is $140.50; and the least unit cost is $153.50. The lowest
cost was obtained using the least total cost method of $140.50. If there were more than eight
weeks, the lowest cost could differ.
The advantage of the least unit cost method is that it is a more complete analysis and
would take into account ordering or setup costs that might change as the order size increases.
If the ordering or setup costs remain constant, the lowest total cost method is more attractive because it is simpler and easier to compute, yet it would be just as accurate under that
restriction.
Concept Connections
LO 21–1 Explain what material requirements planning (MRP) is.
Summary
∙ An enterprise resource planning (ERP) system
­integrates application programs in accounting, sales,
manufacturing, and the other functions in a firm.
MRP is typically an application within the ERP
system.
∙ MRP is the logic that calculates the number of parts,
components, and other materials needed to produce a
product.
∙ MRP determines detailed schedules that show exactly
what is needed over time.
∙ MRP is most useful in industries where standard products are made in batches from common components
and parts.
∙ The master production schedule (MPS) is a plan that
specifies what will be made by a production system in
the future.
∙ The items scheduled in the MPS are referred to as
“end items” and represent the products that drive the
requirements for the MRP system.
∙ The MPS is a plan for meeting all the demands for the
end items, including customer demand, the demand for
replacements, and any other demands that might exist.
∙ Often, “time fences” are used in the MPS to make
the schedules calculated by the MRP system stable
and ensure their feasibility. When the MPS is based
on forecast demand, rather than actual demand, a feature known as “available to promise” is often used
that identifies the difference between the number of
units included in the MPS and current actual customer
orders (these may be different because the forecast may
be different than actual customer demand). This can be
useful for coordinating sales and production activities.
Key Terms
Enterprise resource planning (ERP) A computer system
that integrates application programs in accounting, sales,
manufacturing, and the other functions in a firm. This
integration is accomplished through a database shared
by all the application programs.
Material requirements planning (MRP) The logic for
determining the number of parts, components, and materials needed to produce a product.
Master production schedule (MPS) A time-phased plan
specifying how many of each end item the firm plans to
build and when.
Available to promise A feature of MRP systems that
identifies the difference between the number of units
currently included in the master schedule and the actual
(firm) customer orders.
Material Requirements Planning
Chapter 21
577
LO 21–2 Understand how the MRP system is structured.
Summary
∙ The MRP system uses three sources of information:
1. Demand comes from the master schedule.
2. The bill-of-materials identifies exactly what is
needed to make each end item.
3. The current inventory status of the items managed by
the system (units currently on-hand, expected receipts
in the future, and how long it takes to replenish an
item).
∙ Using the three sources of information, the MRP system produces schedules for each item it manages.
∙ The MRP system can be updated in real time or periodically, depending on the application.
Key Terms
Bill-of-Materials (BOM) The complete product descrip-
tion, listing the materials, parts, and components; the
quantity of each item; and also the sequence in which
the product is created.
Net change systems MRP systems that calculate the
impact of a change in the MRP data (the inventory status, BOM, or master schedule) immediately.
LO 21–3 Analyze an MRP problem.
Summary
∙ The logic used by MRP is often referred to as explosion calculations because the requirements shown in
the MPS are “exploded” into detailed schedules for
each item managed by the system.
∙ The basic logic is that the projected available balance in
this period is calculated by taking the balance from the
last period, subtracting the gross requirements from this
period, and adding in scheduled and planned receipts.
LO 21–4 Evaluate and compare MRP lot-sizing techniques.
Summary
∙ Lot sizes are the production (or purchasing) quantities
used by the MRP system.
∙ Lot-for-lot is the simplest case and is when the system
schedules exactly what is needed in each period.
∙ When setup cost is significant or other constraints
force different quantities, lot-for-lot might not be the
best method to use.
∙ Lot-size techniques are used to balance the fixed and variable costs that vary according to the production lot size.
Solved Problems
LO 21–3
SOLVED PROBLEM 1
Product X is made of two units of Y and three of Z. Y is made of one unit of A and two units
of B. Z is made of two units of A and four units of C.
Lead time for X is one week; Y, two weeks; Z, three weeks; A, two weeks; B, one week;
and C, three weeks.
a. Draw the bill-of-materials (product structure tree).
b. If 100 units of X are needed in week 10, develop a planning schedule showing when each
item should be ordered and in what quantity. Assume we have no inventory in any of the
items to start.
578
Section 4
Supply and Demand Planning and Control
Solution
a. X
Y (2)
Z (3)
A (1)
B (2)
3
X
LT = 1
Y
LT = 2
Z
LT = 3
A
LT = 2
B
LT = 1
C
LT = 3
A (2)
4
5
C (4)
6
7
8
200
200
10
100
100
200
300
600
9
300
600
200
400
400
1,200
1,200
b. The orders are circled.
SOLVED PROBLEM 2
Product M is made of two units of N and three of P. N is made of two units of R and four units
of S. R is made of one unit of S and three units of T. P is made of two units of T and four
units of U.
a. Show the bill-of-materials (product structure tree).
b. If 100 Ms are required, how many units of each component are needed?
c. Show both a single-level parts list and an indented parts list.
Solution
a. M
N (2)
R (2)
S (1)
b. M = 100
N = 200
P = 300
R = 400
P (3)
S (4)
T (2)
T (3)
S = 800 + 400 = 1,200
T = 600 + 1,200 = 1,800
U = 1,200
U (4)
Material Requirements Planning
579
Chapter 21
c. Single-Level
Parts List
Indented Parts List
M
N (2)
N(2)
P (3)
R(2)
N
S (1)
R (2)
T (3)
S (4)
R
S (4)
P (3)
S (1)
T (2)
T (3)
U (4)
P
T (2)
U (4)
SOLVED PROBLEM 3
Given the product structure diagram, and the data given, complete the MRP records for parts
A, B, and C.
A
C
B (2)
C
Week
Item
A
LT = 1 week
On-hand = 21
Safety stock = 0
Order quantity = 20
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned-order receipts
Planned-order releases
B
LT = 2 weeks
On-hand = 20
Safety stock = 0
Order quantity = 40
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned-order receipts
Planned-order releases
C
LT = 1 week
On-hand = 70
Safety Stock = 10
Order quantity = lot-for-lot
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned-order receipts
Planned-order releases
1
2
3
4
5
6
5
15
18
8
12
22
32
580
Supply and Demand Planning and Control
Section 4
Solution
Week
Item
A
LT = 1 week
On-hand = 21
Safety stock = 0
Order quantity = 20
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned-order receipts
Planned-order releases
B
LT = 2 weeks
On-hand = 20
Safety stock = 0
Order quantity = 40
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned-order receipts
Planned-order releases
C
LT = 1 week
On-hand = 70
Safety Stock = 10
Order quantity = lot-for-lot
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned-order receipts
Planned-order releases
1
2
3
5
6
5
15
18
8
12
22
16
1
15
5
20
3
1
19
20
20
3
17
20
20
40
40
12
12
28
40
40
40
20
60
20
0
0
60
60
32
52
40
60
4
20
40
12
12
28
40
12
20
0
0
20
20
0
20
Notes:
1. For item A, start by calculating the projected available balance through week 2. In week
3, there is a net requirement for 17 units, so we plan to receive an order for 20 units. Projected available balance for week 3 is three units and a net requirement for five in week 4,
so we plan another order to be received in week 4. Projected available balance for week 4
is 15 units, with three in week 5 and a net requirement for 19 in week 6. We need to plan
one more order for receipt in week 6.
2. The gross requirements for B are based on two times the planned order releases for A. We
need to account for the scheduled receipt in week 1 of 32 units, resulting in a projected
available balance of 52 at the end of week 1.
3. The gross requirements for C are based on the planned order releases for items A and B
because C is used in both items. The projected available balance is calculated by subtracting out the safety stock because this inventory is kept in reserve. In week 1, for example,
projected available balance is 70 units on-hand − 40 units gross requirements − 10 units
safety stock = 20 units.
LO 21–4
SOLVED PROBLEM 4
Consider the following data relevant to an MRP lot-sizing problem:
Item cost per unit
$25
Setup cost
$100
Inventory carrying cost per year
20.8%
Weekly Net Requirements
1
2
3
4
5
6
7
8
105
80
130
50
0
200
125
100
Use the four lot-sizing rules in the chapter to propose an MRP schedule under each rule.
Assume there is no beginning inventory.
Solution
Lot-for-Lot
The lot-for-lot rule is very commonly used because it is so simple and intuitive. The plannedorder quantities are equal to the net requirements each week.
Material Requirements Planning
581
Chapter 21
Week
Requirements
Net
Production
Quantity
Ending
Inventory
Holding
Cost
Setup
Cost
Total
Cost
1
105
105
0
$0.00
$100.00
$100.00
2
80
80
0
0.00
100.00
200.00
3
130
130
0
0.00
100.00
300.00
4
50
50
0
0.00
100.00
400.00
5
0
0
0
0.00
0.00
400.00
6
200
200
0
0.00
100.00
500.00
7
125
125
0
0.00
100.00
600.00
8
100
100
0
0.00
100.00
700.00
Economic Order Quantity
We need D, S, and H in the EOQ formula. We will estimate annual demand based on average
weekly demand over these 8 weeks.
105 + 80 + 130 + 50 + 0 + 200 + 125 + 100
​D = Annual demand =
​ ____________________________________
​
× 52 = 5, 135​
8
​H = Annual holding cost = .208 × $25.00 = $5.20​
​S = Setup cost = $100
____
(given )​
____________
2(5135 )(100 )
​EOQ = ​ ____
​  2DS ​ ​ = ​ ____________
​
​ ​ = 444​
H
5.20
√
√
In computing holding costs per week, divide H by 52. Weekly holding cost is $0.10 per unit.
We can now develop an order schedule based on EOQ lot sizing.
Week
Net
Requirements
Production
Quantity
Ending
Inventory
Holding
Cost
Setup
Cost
Total
Cost
1
105
444
339
$33.90
$100.00
$133.90
2
80
0
259
25.90
0.00
159.80
3
130
0
129
12.90
0.00
172.70
4
50
0
79
7.90
0.00
180.60
5
0
0
79
7.90
0.00
188.50
6
200
444
323
32.30
100.00
320.80
7
125
0
198
19.80
0.00
340.60
8
100
0
98
9.80
0.00
350.40
Least Total Cost (LTC)
Similar to the example in Exhibit 21.15, we can create the following table comparing costs for
ordering 1 through 8 weeks’ demand in the first order.
Weeks
Net
Requirements
Production
Quantity
Holding
Cost
Setup
Cost
Total
Cost
1
105
105
$ 0.00
$100.00
$100.00
1−2
80
185
8.00
100.00
108.00
1−3
130
315
34.00
100.00
134.00
1−4
50
365
49.00
100.00
149.00
1−5
0
365
49.00
100.00
149.00
1−6
200
565
149.00
100.00
249.00
1−7
125
690
224.00
100.00
324.00
1−8
100
790
294.00
100.00
394.00
7
125
125
0.00
100.00
100.00
7−8
100
225
10.00
100.00
110.00
582
Supply and Demand Planning and Control
Section 4
For the first order, the difference between holding and setup costs is least when ordering for
weeks 1 through 6, so the first order should be for 565 units, enough for weeks 1 through 6. For
the second order, we need to consider only weeks 7 and 8. The difference between holding and
setup costs is least when placing a second order to cover demand during weeks 7 through 8,
so the second order should be for 225 units. Note that as we move through time and net requirements for weeks 9 and beyond become known, we would revisit the second order based on those
new requirements. It is likely that the best second order will end up being for more than just
weeks 7 and 8. For now, we can develop an order schedule based on the data we have available.
Week
Net
Requirements
Production
Quantity
Ending
Inventory
Holding
Cost
Setup
Cost
Total
Cost
1
105
565
460
$46.00
$100.00
$146.00
2
80
0
380
38.00
0.00
184.00
3
130
0
250
25.00
0.00
209.00
4
50
0
200
20.00
0.00
229.00
5
0
0
200
20.00
0.00
249.00
6
200
0
0
0.00
0.00
249.00
7
125
225
100
10.00
100.00
359.00
8
100
0
0
0.00
0.00
359.00
Least Unit Cost (LUC)
The LUC method uses calculations from the LTC method, dividing each option’s total cost by
the order quantity to determine a unit cost. Most of the following table is copied from the LTC
method, with one additional column to calculate the unit costs.
Week
Net
Requirements
Production
Quantity
Holding
Cost
Setup
Cost
Total
Cost
Unit
Cost
1
105
105
$ 0.00
$100.00
$100.00
$0.9524
1−2
80
185
8.00
100.00
108.00
0.5838
1−3
130
315
34.00
100.00
134.00
0.4254
1−4
50
365
49.00
100.00
149.00
0.4082
1−5
0
365
49.00
100.00
149.00
0.4082
1−6
200
565
149.00
100.00
249.00
0.4407
1−7
125
690
224.00
100.00
324.00
0.4696
1−8
100
790
294.00
100.00
394.00
0.4987
6
200
200
0.00
100.00
100.00
0.5000
6−7
125
325
12.50
100.00
112.50
0.3462
6−8
100
425
32.50
100.00
132.50
0.3118
For the first order, the least unit cost results from ordering enough to cover weeks 1
through 5, so our first order would be for 365 units. (This example can be a bit tricky—we
have to use a little common sense.) Ordering for weeks 1 through 4 has the same low unit cost
because there is no demand for week 5. We will say we are ordering for weeks 1 through 5
so that we don’t place an unnecessary order in week 5 to cover demand for weeks 5 through
8. For the second order, the lowest unit cost comes from ordering for weeks 6 through 8, so
we would plan for an order of 425 units. As with the LTC example, our second order might
change as we learn net requirements for weeks 9 and beyond. Based on these orders, we can
now develop an order schedule based on LUC.
Week
Net
Requirements
Production
Quantity
Ending
Inventory
Holding
Cost
Setup
Cost
Total
Cost
1
105
365
260
$26.00
$100.00
$126.00
2
80
0
180
18.00
0.00
144.00
3
130
0
50
5.00
0.00
149.00
Material Requirements Planning
583
Chapter 21
4
50
0
0
0.00
0.00
149.00
5
0
0
0
0.00
0.00
149.00
6
200
425
225
22.50
100.00
271.50
7
125
0
100
10.00
0.00
281.50
8
100
0
0
0.00
0.00
281.50
Best Lot Size Method
Based on the data we have available, the total costs for each lot-sizing method are lot-for-lot,
$700.00; EOQ, $350.40; LTC, $359.00; and LUC, $281.50. The relatively high setup cost in
this example makes lot-for-lot an unwise choice. LUC has the lowest total cost by a significant margin. It works so well here because it minimizes holding costs across the planning
horizon.
Discussion Questions
LO 21–1
LO 21–2
1.
2.
3.
4.
5.
6.
LO 21–3
7.
8.
9.
10.
11.
LO 21–4
12.
13.
What do we mean when we say that MRP is based on dependent demand?
Discuss the importance of the master production schedule in an MRP system.
Explain the need for time fences in the master production schedule.
“MRP just prepares shopping lists. It does not do the shopping or cook the dinner.”
Comment.
What are the sources of demand in an MRP system? Are these dependent or independent,
and how are they used as inputs to the system?
State the types of data that would be carried in the bill-of-materials file and the inventory
record file.
Discuss the meaning of MRP terms such as planned order release and scheduled order
receipt.
Why is the MRP process referred to as an “explosion”?
Many practitioners currently update MRP weekly or biweekly. Would it be more valuable
if it were updated daily? Discuss.
Should safety stock be necessary in an MRP system with dependent demand? If so, why?
If not, why do firms carry it anyway?
Contrast the significance of the term lead time in the traditional EOQ context and in an
MRP system.
Planning orders using a lot-for-lot (L4L) technique is commonly done because it is simple
and intuitive. It also helps minimize holding costs because you are only ordering what is
needed when it is needed. So far, it sounds like a good idea. Are there any disadvantages
to this approach?
What is meant when we say that the least total cost (LTC) and least unit cost (LUC) methods are dynamic lot-sizing techniques?
Objective Questions
LO 21–1
1. Match the industry type to the expected benefits from an MRP system as High, Medium,
or Low.
Industry Type
Assemble-to-stock
Assemble-to-order
Make-to-stock
Make-to-order
Engineer-to-order
Process
Expected Benefit
(High, Medium, or Low)
584
Supply and Demand Planning and Control
Section 4
LO 21–2
LO 21–3
2. MRP is based on what type of demand?
3. Which scheduling process drives requirements in the MRP process?
4. What term is used to identify the difference between the number of units of an item listed
on the master schedule and the number of firm customer orders?
5. What are the three primary data sources used by the MRP system?
6. What is another common name for the bill-of-materials?
7. What is the process used to ensure that all of the needs for a particular item are calculated
at the same time in the MRP process?
8. What is the MRP term for the time periods used in planning?
Note: For these problems, to simplify data handling to include the receipt of orders that have
actually been placed in previous periods, the following six-level scheme can be used. (A
number of different techniques are used in practice, but the important issue is to keep track
of what is on-hand, what is expected to arrive, what is needed, and what size orders should
be placed.) One way to calculate the numbers is as follows:
Week
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned-order receipt
Planned-order release
9. Semans is a manufacturer that produces bracket assemblies. Demand for bracket assemblies (X) is 130 units. The following is the BOM in indented form:
Item
Description
X
Bracket assembly
1
A
Wall board
4
B
Hanger subassembly
2
D
Hanger casting
3
E
Ceramic knob
1
Rivet head screw
3
F
Metal tong
4
G
Plastic cap
2
C
Usage
The following is a table indicating current inventory levels:
Item
X
A
B
C
D
E
F
G
Inventory
25
16
60
20
180
160
1,000
100
a. Using Excel, create the MRP using the information provided.
b. What are the net requirements of each item in the MPS?
10. In the following MRP planning schedule for item J, indicate the correct net requirements,
planned-order receipts, and planned-order releases to meet the gross requirements. Lead
time is one week.
Week Number
Item J
0
Gross requirements
On-hand
Net requirements
Planned-order receipt
Planned-order release
1
2
75
40
3
4
5
50
70
Material Requirements Planning
Chapter 21
585
11. Assume that product Z is made of two units of A and four units of B. A is made of three
units of C and four of D. D is made of two units of E.
Lead times for the purchase or fabrication of each unit to final assembly are: Z takes
two weeks; A, B, C, and D take one week each; and E takes three weeks.
Fifty units are required in period 10. (Assume that there is currently no inventory onhand of any of these items.)
a. Show the bill-of-materials (product structure tree). (Answer in Appendix D)
b. Develop an MRP planning schedule showing gross and net requirements and order
release and order receipt dates.
12. One unit of A is made of three units of B, one unit of C, and two units of D. B is composed of two units of E and one unit of D. C is made of one unit of B and two units of E.
E is made of one unit of F.
Items B, C, E, and F have one-week lead times; A and D have lead times of two weeks.
Assume that lot-for-lot (L4L) lot sizing is used for items A, B, and F; lots of size 50,
50, and 200 are used for Items C, D, and E, respectively. Items C, E, and F have on-hand
(beginning) inventories of 10, 50, and 150, respectively; all other items have zero beginning inventory. We are scheduled to receive 10 units of A in week 2, 50 units of E in week
1, and also 50 units of F in week 1. There are no other scheduled receipts. If 30 units of
A are required in week 8, use the low-level-coded bill-of-materials to find the necessary
planned-order releases for all components.
13. One unit of A is made of two units of B, three units of C, and two units of D. B is composed of one unit of E and two units of F. C is made of two units of F and one unit of D.
E is made of two units of D. Items A, C, D, and F have one-week lead times; B and E
have lead times of two weeks. Lot-for-lot (L4L) lot sizing is used for items A, B, C, and
D; lots of size 50 and 180 are used for items E and F, respectively. Item C has an on-hand
(beginning) inventory of 15; D has an on-hand inventory of 50; all other items have zero
beginning inventories. We are scheduled to receive 20 units of item E in week 2; there are
no other scheduled receipts.
Construct simple and low-level-coded bill-of-materials (product structure tree) and
indented and summarized parts lists.
If 20 units of A are required in week 8, use the low-level-coded bill-of-materials to find
the necessary planned-order releases for all components.
14. One unit of A is made of one unit of B and one unit of C. B is made of four units of C and
one unit each of E and F. C is made of two units of D and one unit of E. E is made of three
units of F. Item C has a lead time of one week; items A, B, E, and F have two-week lead
times; and item D has a lead time of three weeks. Lot-for-lot (L4L) lot sizing is used for
items A, D, and E; lots of size 50, 100, and 50 are used for items B, C, and F, respectively.
Items A, C, D, and E have on-hand (beginning) inventories of 20, 50, 100, and 10, respectively; all other items have zero beginning inventory. We are scheduled to receive 10 units
of A in week 1, 100 units of C in week 1, and 100 units of D in week 3; there are no other
scheduled receipts. If 50 units of A are required in week 10, use the low-level-coded billof-materials (product structure tree) to find the necessary planned-order releases for all
components.
15. One unit of A is made of two units of B and one unit of C. B is made of three units of D
and one unit of F. C is composed of three units of B, one unit of D, and four units of E. D
is made of one unit of E. Item C has a lead time of one week; items A, B, E, and F have
two-week lead times; and item D has a lead time of three weeks. Lot-for-lot (L4L) lot sizing is used for items C, E, and F; lots of size 20, 40, and 160 are used for items A, B, and
D, respectively. Items A, B, D, and E have on-hand (beginning) inventories of 5, 10, 100,
and 100, respectively; all other items have zero beginning inventories. We are scheduled
to receive 10 units of A in week 3, 20 units of B in week 7, 40 units of F in week 5, and
60 units of E in week 2; there are no other scheduled receipts. If 20 units of A are required
in week 10, use the low-level-coded bill-of-materials (product structure tree) to find the
necessary planned order releases for all components.
586
Section 4
Supply and Demand Planning and Control
16. One unit of A is composed of two units of B and three units of C. Each B is composed of
one unit of F. C is made of one unit of D, one unit of E, and two units of F. Items A, B, C,
and D have 20, 50, 60, and 25 units of on-hand inventory, respectively. Items A, B, and
C use lot-for-lot (L4L) as their lot-sizing technique, while D, E, and F require multiples
of 50, 100, and 100, respectively, to be purchased. B has scheduled receipts of 30 units in
period 1. No other scheduled receipts exist. Lead times are one period for items A, B, and
D, and two periods for items C, E, and F. Gross requirements for A are 20 units in period
1, 20 units in period 2, 60 units in period 6, and 50 units in period 8. Find the planned
order releases for all items.
17. Each unit of A is composed of one unit of B, two units of C, and one unit of D. C is composed of two units of D and three units of E. Items A, C, D, and E have on-hand inventories of 20, 10, 20, and 10 units, respectively. Item B has a scheduled receipt of 10 units
in period 1, and C has a scheduled receipt of 50 units in period 1. Lot-for-lot (L4L) lot
sizing is used for items A and B. Item C requires a minimum lot size of 50 units. D and
E are required to be purchased in multiples of 100 and 50, respectively. Lead times are
one period for items A, B, and C, and two periods for items D and E. The gross requirements for A are 30 in period 2, 30 in period 5, and 40 in period 8. Find the planned-order
releases for all items.
18. Product A is an end item and is made from two units of B and four of C. B is made of
three units of D and two of E. C is made of two units of F and two of E.
A has a lead time of one week. B, C, and E have lead times of two weeks, and D and F
have lead times of three weeks.
a. Show the bill-of-materials (product structure tree).
b. If 100 units of A are required in week 10, develop the MRP planning schedule, specifying when items are to be ordered and received. There are currently no units of inventory on-hand.
19. Audio Products, Inc., produces two AM/FM/CD players for cars. The radio/CD units are
identical, but the mounting hardware and finish trim differ. The standard model fits intermediate and full-sized cars, and the sports model fits small sports cars.
Audio Products handles the production in the following way. The chassis (radio/CD
unit) is assembled in Mexico and has a manufacturing lead time of two weeks. The
mounting hardware is purchased from a sheet steel company and has a three-week lead
time. The finish trim is purchased as prepackaged units consisting of knobs and various
trim pieces from a Taiwan electronics company with offices in Los Angeles. Trim packages have a two-week lead time. Final assembly time may be disregarded because adding
the trim package and mounting are performed by the customer.
Audio Products supplies wholesalers and retailers, which place specific orders for both
models up to eight weeks in advance. These orders, together with enough additional units
to satisfy the small number of individual sales, are summarized in the following demand
schedule.
Week
Model
Standard model
Sports model
1
2
3
4
5
300
6
7
8
400
200
100
There are currently 50 radio/CD units on-hand but no trim packages or mounting
hardware.
Prepare a material requirements plan to meet the demand schedule exactly. Specify the
gross and net requirements, on-hand amounts, and the planned order release and receipt
periods for the radio/CD chassis, the standard trim and sports car model trim, and the
standard mounting hardware and the sports car mounting hardware.
Material Requirements Planning
LO 21–4
587
Chapter 21
20. The MRP gross requirements for item A are shown here for the next 10 weeks. Lead time
for A is three weeks and setup cost is $10. There is a carrying cost of $0.01 per unit per
week. Beginning inventory is 90 units.
Week
Gross
requirements
1
2
3
4
5
6
7
8
9
10
30
50
10
20
70
80
20
60
200
50
se the least total cost or the least unit cost lot-sizing method to determine when and for
U
what quantity the first order should be released.
21. The MRP gross requirements for item X are shown here for the next 10 weeks. Lead time
for A is two weeks, and setup cost is $9. There is a carrying cost of $0.02 per unit per
week. Beginning inventory is 70 units.
Week
Gross
requirements
1
2
3
4
5
6
7
8
9
10
20
10
15
45
10
30
100
20
40
150
se the least total cost or the least unit cost lot-sizing method to determine when and for
U
what quantity the first order should be released. (Answer in Appendix D)
22. Product A consists of two units of subassembly B, three units of C, and one unit of D. B
is composed of four units of E and three units of F. C is made of two units of H and three
units of D. H is made of five units of E and two units of G.
a. Construct a simple bill-of-materials (product structure tree).
b. Construct a product structure tree using low-level coding.
c. Construct an indented parts list.
d. To produce 100 units of A, determine the number of units of B, C, D, E, F, G, and H
required.
Analytics Exercise: An MRP Explosion—Brunswick Motors
Recently, Phil Harris, the production control manager at
Brunswick, read an article on time-phased requirements
planning. He was curious about how this technique might
work in scheduling Brunswick’s engine assembly operations and decided to prepare an example to illustrate the
use of time-phased requirements planning.
Phil’s first step was to prepare a master schedule
for one of the engine types produced by Brunswick: the
Model 1000 engine. This schedule indicates the number of units of the Model 1000 engine to be assembled
each week during the last 12 weeks and is shown on the
next page. Next, Phil decided to simplify his requirements planning example by considering only two of the
many components needed to complete the assembly of
the Model 1000 engine. These two components, the gear
box and the input shaft, are shown in the product structure diagram shown below. Phil noted that the gear box
is assembled by the Subassembly Department and subsequently is sent to the main engine assembly line. The input
shaft is one of several component parts manufactured by
Brunswick needed to produce a gear box subassembly.
Thus, levels 0, 1, and 2 are included in the product structure diagram to indicate the three manufacturing stages
involved in producing an engine: the Engine Assembly Department, the Subassembly Department, and the
Machine Shop.
The manufacturing lead times required to produce
the gear box and input shaft components are also indicated in the bill-of-materials diagram. Note that two
weeks are required to produce a batch of gear boxes and
that all the gear boxes must be delivered to the assembly
line parts stockroom before Monday morning of the week
in which they are to be used. Likewise, it takes three
weeks to produce a lot of input shafts, and all the shafts
needed for the production of gear boxes in a given week
must be delivered to the Subassembly Department stockroom before Monday morning of that week.
In preparing the MRP example, Phil planned to use
the worksheets shown on the next page and to make the
following assumptions:
1. Seventeen gear boxes are on-hand at the beginning
of week 1, and five gear boxes are currently on
order to be delivered at the start of week 2.
2. Forty input shafts are on-hand at the start of week
1, and 22 are scheduled for delivery at the beginning of week 2.
588
Supply and Demand Planning and Control
Section 4
Model 1000 master schedule
Week
1
2
3
4
Demand 15
5
7
10
5
6
7
8
15
20
10
9
10
11
12
8
2
16
Model 1000 product structure
Engine assembly
Gear box
Lead time = 2 weeks
Used: 1 per engine
Crankcase
Input shaft
Lead time = 3 weeks
Used: 2 per gear box
carrying and setup for the gear boxes and input
shafts. These costs are as follows:
Assignment
Part
Cost
Gear Box
Setup = $90/order
Inventory carrying cost = $2/unit/week
1. Initially, assume that Phil wants to minimize his
inventory requirements. Assume that each order
will be only for what is required for a single
period. Using the following forms, calculate the
net requirements and planned order releases for the
gear boxes and input shafts. Assume that lot sizing
is done using lot-for-lot.
2. Phil would like to consider the costs that his
accountants are currently using for inventory
Setup = $45/order
Input Shaft
Inventory carrying cost = $1/unit/week
Given the cost structure, evaluate the cost of the
schedule from (1). Assume inventory is valued at
the end of each week.
3. Find a better schedule by reducing the number of
orders and carrying some inventory. What are the
cost savings with this new schedule?
Engine assembly master schedule
Week
1
2
3
4
5
6
7
8
9
10
11
12
8
9
10
11
12
8
9
10
11
12
Quantity
Gear box requirements
Week
1
2
3
4
5
6
7
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned order release
Input shaft requirements
Week
Gross requirements
Scheduled receipts
Projected available balance
Net requirements
Planned order release
1
2
3
4
5
6
7
Material Requirements Planning
Chapter 21
589
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. Term used for a computer system that integrates application programs for the different functions in a firm.
2. Logic used to calculate the needed parts, components,
and other materials needed to produce an end item.
3. This drives the MRP calculations and is a detailed
plan for how we expect to meet demand.
4. Period of time during which a customer has a specified level of opportunity to make changes.
5. This identifies the specific materials used to make
each item and the correct quantities of each.
6. If an item is used in two places in a bill-of-materials,
say level 3 and level 4, what low-level code would be
assigned to the item?
7. One unit of part C is used in item A and in item
B. Currently, we have 10 As, 20 Bs, and 100 Cs in
8.
9.
10.
11.
12.
13.
14.
inventory. We want to ship 60 As and 70 Bs. How
many additional Cs do we need to purchase?
These are orders that have already been released and
are to arrive in the future.
This is the total amount required for a particular item.
This is the amount needed after considering what we
currently have in inventory and what we expect to
arrive in the future.
The planned-order receipt and planned-order release
are offset by this amount of time.
These are the part quantities issued in the plannedorder release section of an MRP report.
The term for ordering exactly what is needed each
period without regard to economic considerations.
None of the techniques for determining order quantity consider this important noneconomic factor that
could make the order quantity infeasible.
Answers to Practice Exam 1. Enterprise resource planning (ERP) 2. Material requirements planning (MRP) 3. Master production schedule
4. Time fence 5. Bill-of-materials 6. Level 4 7. Zero 8. Scheduled receipts 9. Gross requirements 10. Net requirements 11. Lead time 12. Lot
sizes 13. Lot-for-lot ordering 14. Capacity
22
Workcenter
Scheduling
Learning Objectives
LO22–1
LO22–2
LO22–3
LO22–4
Explain workcenter scheduling.
Analyze scheduling problems using priority rules and more specialized techniques.
Apply scheduling techniques to the manufacturing shop floor.
Analyze employee schedules in the service sector.
HOSPITALS CUT ER WAITS—NEW “FAST
TRACK” UNITS, HIGH-TECH IDS SPEED VISITS
A few years ago, Oakwood Hospital and Medical Center in Dearborn, Michigan, promised that anybody taken to the emergency department would be seen by a doctor
within 30 minutes—or they would get a written apology and two free movie passes. It
sounded like a cheap marketing ploy. Some employees cringed.
The 30-minute guarantee has been a huge success.
All four of Oakwood Healthcare System’s hospitals rolled
it out, and patient satisfaction levels soared. Less than 1
percent of the patients asked for free tickets.
Recently, the center announced a zero-wait program
in the four hospital emergency departments and at Oakwood’s health care center. Success with this precedentsetting service is not yet known, but processes were
redesigned and some tricky scheduling of staff is being
employed.
A growing number of hospitals are putting patients
with relatively minor ailments—who previously would
be left to languish in the waiting room—into “fast track”
units to get them in and out of emergency beds quickly.
Others are using sophisticated computer systems to give
Patients in a hospital
waiting room.
administrators a complete up-to-the-minute status report on every patient in every
© Heath Korvola/Getty
Images RF
emergency bed. In some areas, medical identification cards are being used that can
590
be swiped into a computer to speed up patient registrations and produce instant vital
information to emergency doctors and nurses. Other changes needed to slash waiting times require reengineering billing, records, and laboratory operations; upgrading technical staff; and replacing the emergency physician group with a new crew
willing to work longer hours.
WO R KCENTER SCHEDULING
Keep in mind that workflow equals cash flow, and scheduling lies at the heart of the process.
A schedule is a timetable for performing activities, utilizing resources, or allocating facilities.
In this chapter, we discuss short-run scheduling and control of orders with an emphasis on
workcenters. We also introduce some basic approaches to short-term scheduling of workers
in services.
Operations scheduling is at the heart of what is currently referred to as Manufacturing
Execution Systems (MES). An MES is an information system that schedules, dispatches,
tracks, monitors, and controls production on the factory floor. Such systems also provide
real-time linkages to MRP systems, product and process planning, and systems that extend
beyond the factory, including supply chain management, ERP, sales, and service management. A number of software specialty houses develop and implement MESs as part of a suite
of software tools.
Similar to an MES, a Service Execution System (SES) is an information system that links,
schedules, dispatches, tracks, monitors, and controls the customer’s encounters with the service organization and its employees. Obviously, the extent to which each of these elements
is brought into play is determined by the extent of the customer’s physical involvement with
the service organization, the number of stages in the service, and whether the service is standardized (e.g., a scheduled airline flight) or customized (e.g., a hospital visit). The common
features of any large system are a central database that contains all the relevant information
on resource availability and customers, and a management control function that integrates and
oversees the process.
LO 22–1
Explain workcenter
scheduling.
Manufacturing
Execution System
(MES)
An information system that
schedules, dispatches,
tracks, monitors, and
controls production on the
factory floor.
T h e N a t ur e a nd Im por t a n ce o f Wo rkcen ters
A workcenter is an area in a business in which productive resources are organized and work
is completed. The workcenter may be a single machine, a group of machines, or an area where
a particular type of work is done. These workcenters can be organized according to function
in a workcenter configuration or by-product in a flow, assembly line, or group technology cell
(GT cell) configuration. Recall from the discussion in Chapter 8 that many firms have moved
from the workcenter configuration to GT cells.
In the case of the workcenter, jobs need to be routed between functionally organized workcenters to complete the work. When a job arrives at a workcenter—for example, the drilling
department in a factory that makes custom-printed circuit boards—it enters a queue to wait
for a drilling machine that can drill the required holes. Scheduling, in this case, involves determining the order for running the jobs, and also assigning a machine that can be used to make
the holes.
A characteristic that distinguishes one scheduling system from another is how capacity is considered in determining the schedule. Scheduling systems can use either infinite
or finite loading. Infinite loading occurs when work is assigned to a workcenter simply
based on what is needed over time. No consideration is given directly to whether there
is sufficient capacity at the resources required to complete the work, nor is the actual
sequence of the work as done by each resource in the workcenter considered. Often, a
simple check is made of key resources to see if they are overloaded in an aggregate sense.
This is done by calculating the amount of work required over a period (usually a week)
Workcenter
Often referred to as a job
shop, a process structure
suited for low-volume
production of a great
variety of nonstandard
products. Workcenters
sometimes are referred to
as departments and are
focused on a particular
type of operation.
Infinite loading
Work is assigned to a
workcenter based on
what is needed over time.
Capacity is not considered.
591
592
Section 4
Finite loading
Each resource is scheduled
in detail using the setup
and run time required for
each order. The system
determines exactly what
will be done by each
resource at every moment
during the working day.
Forward scheduling
Schedules from now
into the future to tell the
earliest that an order can
be completed.
Backward scheduling
Starts from some date in
the future (typically the
due date) and schedules
the required operations in
reverse sequence. Tells the
latest time when an order
can be started so that it is
completed by a specific
date.
Machine-limited
process
Equipment is the critical
resource that is scheduled.
Labor-limited process
People are the key
resource that is scheduled.
At kaiten sushi
restaurants, sushi is
circulated to customers
on a conveyor belt. In
order to monitor the
quality of the product,
some Kaiten Sushi
restaurants use RFID
tagging.
© sozaijiten/Datacraft/Getty
Images RF
Supply and Demand Planning and Control
using setup and run time standards for each order. When using an infinite loading system,
lead time is estimated by taking a multiple of the expected operation time (setup and run
time) plus an expected queuing delay caused by material movement and waiting for the
order to be worked on.
A finite loading approach actually schedules in detail each resource using the setup and
run time required for each order. In essence, the system determines exactly what will be done
by each resource at every moment during the working day. If an operation is delayed due to
a part(s) shortage, the order will sit in the queue and wait until the part is available from a
preceding operation. Theoretically, all schedules are feasible when finite loading is used.
Another characteristic that distinguishes scheduling systems is whether the schedule is
generated forward or backward in time. For this forward–backward dimension, the most common is forward scheduling. Forward scheduling refers to the situation in which the system
takes an order and then schedules each operation that must be completed forward in time. A
system that forward schedules can tell the earliest date that an order can be completed. Conversely, backward scheduling starts from some date in the future (possibly a due date) and
schedules the required operations in reverse sequence. This tells the latest time when an order
can be started so that it is completed by a specific date.
A material requirements planning (MRP) system is an example of an infinite loading,
backward scheduling system for materials. With simple MRP, each order has a due date sometime in the future. In this case, the system calculates parts needs by backward scheduling
the time that the operations will be run to complete the orders. The time required to make
each part (or batch of parts) is estimated based on historical data. The scheduling systems
addressed in this chapter are intended for the processes required to actually make those parts
and subassemblies.
Thus far, the term resources has been used in a generic sense. In practice, we need to
decide what we are going to actually schedule. Commonly, processes are referred to as either
machine limited or labor limited. In a machine-limited process, equipment is the critical
resource that is scheduled. Similarly, in a labor-limited process, people are the key resource
that is scheduled. Most actual processes are either labor limited or machine limited but, luckily, not both.
Workcenter Scheduling
ex hibit 22.1
Chapter 22
593
Types of Manufacturing Processes and Scheduling Approaches
Type
Product
Characteristics
Typical Scheduling Approach
Continuous
process
Chemicals, steel, wire and
cables, liquids (beer, soda),
canned goods
Full automation, low labor content
in product costs, facilities dedicated to one product
Finite forward scheduling of the process;
machine limited
High-volume
manufacturing
Automobiles, telephones, fasteners, textiles, motors, household
fixtures
Automated equipment, partially
automated handling, moving
assembly lines, most equipment
in line
Finite forward scheduling of the line (a
production rate is typical); machine limited;
parts are pulled to the line using just-in-time
(kanban) system
Mid-volume
manufacturing
Industrial parts, high-end
consumer products
GT cells, focused minifactories
Infinite forward scheduling typical: priority control; typically labor limited, but often machine
limited; often responding to just-in-time orders
from customers or MRP due dates
Low-volume
workcenters
Custom or prototype equipment,
specialized instruments, lowvolume industrial products
Machining centers organized by
manufacturing function (not in
line), high labor content in product
cost, general-purpose machinery
with significant changeover time,
little automation of material handling, large variety of product
Infinite, forward scheduling of jobs: usually
labor limited, but certain functions may be
machine limited (a heat-treating process or
a precision machining center, for example);
priorities determined by MRP due dates
Exhibit 22.1 describes the scheduling approaches typically used for different manufacturing processes. Whether capacity is considered depends on the actual process. Available
computer technology allows generation of very detailed schedules such as scheduling each
job on each machine and assigning a specific worker to the machine at a specific point in time.
Systems that capture the exact state of each job and each resource are also available. Using
RFID or bar-coding technology, these systems can efficiently capture all of this detailed
information.
Typ ica l S che duling a nd C o n t ro l F u n ctio n s
The following functions must be performed in scheduling and controlling an operation:
1.
Allocating jobs, equipment, and personnel to workcenters or other specified locations. Essentially, this is short-run capacity planning.
2. Determining the sequence of order performance (that is, establishing job priorities).
3. Initiating performance of the scheduled work. This is commonly termed the
dispatching of jobs.
4. Shop-floor control (or production activity control) involving:
a. Reviewing the status and controlling the progress of jobs as they are being worked on.
b. Expediting late and critical jobs.
A simple workcenter scheduling process is shown in Exhibit 22.2. At the start of the day,
the scheduler (in this case, a production control person assigned to this department) selects
and sequences available jobs to be run at individual workstations. The scheduler’s decisions
would be based on the operations and routing requirements of each job, the status of existing
jobs at each workcenter, the queue of work before each workcenter, job priorities, material
availability, anticipated job orders to be released later in the day, and workcenter resource
capabilities (labor and/or machines).
To help organize the schedule, the scheduler would draw on job status information from the
previous day, external information provided by central production control, process engineering, and so on. The scheduler also would confer with the supervisor of the department about
the feasibility of the schedule, especially workforce considerations and potential bottlenecks.
Dispatching
The activity of initiating
scheduled work.
594
Supply and Demand Planning and Control
Section 4
exhibit 22.2
Typical Scheduling Process
Station 1
Orders
Station 2
Orders
New
orders
Station 4
Production
control
Orders
Supervisor
Station 3
Orders
The details of the schedule are communicated to workers via dispatch lists shown on computer terminals, in hard-copy printouts, or by posting a list of what should be worked on in
central areas. Visible schedule boards are highly effective ways to communicate the priority
and current status of work.
Obje ctive s o f Wo rkcen t er Sch ed u lin g
The objectives of workcenter scheduling are to (1) meet due dates, (2) minimize lead time,
(3) minimize setup time or cost, (4) minimize work-in-process inventory, and (5) maximize
machine or labor utilization. It is unlikely, and often undesirable, to simultaneously satisfy all
of these objectives. For example, keeping all equipment and/or employees busy may result in
having to keep too much inventory. Or, as another example, it is possible to meet 99 out of 100
of your due dates but still have a major schedule failure if the one due date that was missed
was for a critical job or key customer. The important point, as is the case with other production activities, is to maintain a systems perspective to assure that workcenter objectives are in
sync with the operations strategy of the organization.
J ob S e q u e n cin g
Sequencing
The process of determining
which job to start first on a
machine or workcenter.
Priority rules
The logic used to
determine the sequence of
jobs in a queue.
The process of determining the job order on some machine or in some workcenter is known
as sequencing or priority sequencing. Priority rules are the rules used in obtaining a job
sequence. These can be very simple, requiring only that jobs be sequenced according to
one piece of data, such as processing time, due date, or order of arrival. Other rules, though
equally simple, may require several pieces of information, typically to derive an index number
such as the least slack rule and the critical ratio rule (both defined later). Still others, such as
Johnson’s rule (also discussed later), apply to job scheduling on a sequence of machines and
require a computational procedure to specify the order of performance. Eight of the more
common priority rules are shown in Exhibit 22.3.
The following standard measures of schedule performance are used to evaluate priority rules:
1.
2.
3.
4.
Meeting due dates of customers or downstream operations.
Minimizing the flow time (the time a job spends in the process).
Minimizing work-in-process inventory.
Minimizing the idle time of machines or workers.
Workcenter Scheduling
exhibit 22.3
Chapter 22
595
Priority Rules for Job Sequencing
1 FCFS (first come, first served). Orders are run in the order they arrive in the department.
2 SOT (shortest operating time). Run the job with the shortest completion time first, next-shortest second, and so on. This is sometimes also referred to as SPT (shortest processing time). This rule is often
combined with a lateness rule to prevent jobs with longer times from being delayed too long.
3 EDD (earliest due date first). Run the job with the earliest due date first.
4 STR (slack time remaining). This is calculated as the time remaining before the due date minus the
processing time remaining. Orders with the shortest slack time remaining (STR) are run first.
STR = Time remaining before due date — Remaining processing time
5 STR/OP (slack time remaining per operation). Orders with the shortest slack time per number of
operations are run first.
STR/OP = STR/Number of remaining operations
6 CR (critical ratio). This is calculated as the difference between the due date and the current date
divided by the number of work days remaining. Orders with the smallest CR are run first.
7 LCFS (last come, first served). This rule occurs frequently by default. As orders arrive, they are placed
on the top of the stack; the operator usually picks up the order on top to run first.
8 Random order or whim. The supervisors or the operators usually select whichever job they feel like
running.
PRI OR IT Y R ULES AND TECHNIQUES
S c h e d u lin g n Jo bs on On e Mach in e
Let’s look at some of the eight priority rules compared in a static scheduling situation involving four jobs on one machine. (In scheduling terminology, this class of problems is referred
to as an “n job—one-machine problem” or simply “n/1.”) The theoretical difficulty of scheduling problems increases as more machines are considered rather than as more jobs must be
processed; therefore, the only restriction on n is that it be a specified, finite number. Consider
the following example.
EXAMPLE 22.1: n Jobs on One Machine
Mike Morales is the supervisor of Legal Copy-Express, which provides copy services for
downtown Los Angeles law firms. Five customers submitted their orders at the beginning of
the week. Specific scheduling data are as follows:
Job (in Order
of Arrival)
Processing
Time (Days)
Due Date
(Days Hence)
A
3
5
B
4
6
C
2
7
D
6
9
E
1
2
All orders require the use of the only color copy machine available; Morales must decide on
the processing sequence for the five orders. The evaluation criterion is minimum flow time.
Suppose that Morales decides to use the FCFS rule in an attempt to make Legal Copy-Express
appear fair to its customers.
LO 22–2
Analyze scheduling
problems using priority
rules and more specialized
techniques.
596
Section 4
Supply and Demand Planning and Control
SOLUTION
FCFS RULE: The FCFS rule results in the following flow times:
FCFS Schedule
Job
Sequence
Processing
Time (Days)
Due Date
(Days Hence)
Flow
Time (Days)
A
3
5
0+3= 3
B
4
6
3+4= 7
C
2
7
7+2= 9
D
6
9
9 + 6 = 15
E
1
2
15 + 1 = 16
Total flow time = 3 + 7 + 9 + 15 + 16 = 50 days
50
​Average flow time = ___
​   ​ = 10 days​
5
Comparing the due date of each job with its flow time, we observe that only Job A will be on
time. Jobs B, C, D, and E will be late by 1, 2, 6, and 14 days, respectively. On average, a job
will be late by (0 + 1 + 2 + 6 + 14)∕5 = 4.6 days.
SOLUTION
SOT RULE: Let’s now consider the SOT rule. Here, Morales gives the highest priority to the
order that has the shortest processing time. The resulting flow times are
SOT Schedule
Job
Sequence
Processing
Time (Days)
Due Date
(Days Hence)
Flow Time
(Days)
E
1
2
0 + 1 = 1
C
2
7
1 + 2 = 3
A
3
5
3 + 3 = 6
B
4
6
6 + 4 = 10
D
6
9
10 + 6 = 16
Total flow time = 1 + 3 + 6 + 10 + 16 = 36 days
36
​Average flow time = ___
​   ​ = 7.2 days​
5
SOT results in a lower average flow time than the FCFS rule. In addition, Jobs E and C will
be ready before the due date, and Job A is late by only one day. On average, a job will be late
by (0 + 0 + 1 + 4 + 7)∕5 = 2.4 days.
SOLUTION
EDD RULE: If Morales decides to use the EDD rule, the resulting schedule is
EDD Schedule
Job
Sequence
Processing
Time (Days)
Due Date
(Days Hence)
Flow Time
(Days)
E
1
2
0+1= 1
A
3
5
1+3= 4
B
4
6
4+4= 8
C
2
7
8 + 2 = 10
D
6
9
10 + 6 = 16
Total flow time 1 + 4 + 8 + 10 + 16 = 39 days
Average flow time = 7.8 days
Workcenter Scheduling
Chapter 22
In this case, Jobs B, C, and D will be late. On average, a job will be late by (0 + 0 + 2 + 3 +
7)∕5 = 2.4 days.
SOLUTION
LCFS, RANDOM, and STR RULES: Here are the resulting flow times of the LCFS, random,
and STR rules:
Processing
Time (Days)
Due Date
(Days Hence)
E
1
2
0+1= 1
D
6
9
1+6= 7
C
2
7
7+2= 9
B
4
6
9 + 4 = 13
A
3
5
13 + 3 = 16
D
6
9
0+6= 6
C
2
7
6+2= 8
A
3
5
8 + 3 = 11
E
1
2
11 + 1 = 12
B
4
6
12 + 4 = 16
E
1
2
0+1= 1
2−1=1
A
3
5
1+3= 4
5−3=2
B
4
6
4+4= 8
6−4=2
D
6
9
8 + 6 = 14
9−6=3
C
2
7
14 + 2 = 16
7−2=5
Job Sequence
Flow Time
(Days)
LCFS Schedule
Total flow time = 46 days
Average flow time = 9.2 days
Average lateness = 4.0 days
Random Schedule
Total flow time = 53 days
Average flow time = 10.6 days
Average lateness = 5.4 days
STR Schedule
Slack
Total flow time = 43 days
Average flow time = 8.6 days
Average lateness = 3.2 days
Comparison of Priority Rules
Here are some of the results summarized for the rules that Morales examined:
Rule
Total Flow
Time (Days)
Average Flow
Time (Days)
FCFS
50
SOT
36
7.2
2.4
EDD
39
7.8
2.4
LCFS
46
9.2
4.0
Random
53
10.6
5.4
STR
43
8.6
3.2
10
Average Lateness
(Days)
4.6
Here, SOT is better than the other rules in terms of average flow time. Moreover, it can be
shown mathematically that the SOT rule yields an optimal solution in the n/1 case for average
597
598
Supply and Demand Planning and Control
Section 4
flow time and performs well relative to average lateness as well. In fact, so powerful is this
simple rule that it has been termed the most important concept in the entire aspect of sequencing. It does have its shortcomings, however. The main one is that longer jobs may never
be started if short jobs keep arriving at the scheduler’s desk. To avoid this, companies may
invoke what is termed a truncated SOT rule whereby jobs waiting for a specified time period
are automatically moved to the front of the line.
S che dulin g n Jo bs o n Two Mach in es
Johnson’s rule
A sequencing rule used
for scheduling any number
of jobs on two machines.
The rule is designed to
minimize the time required
to complete all the jobs.
The next step up in complexity is the n/2 flow-shop case, where two or more jobs must be
processed on two machines in a common sequence. As in the n/1 case, there is an approach
that leads to an optimal solution according to certain criteria. The objective of this approach,
termed Johnson’s rule or Johnson’s method (after its developer), is to minimize the flow time
from the beginning of the first job until the finish of the last. Johnson’s rule consists of the
following steps:
1.
2.
3.
4.
List the operation time for each job on both machines.
Select the shortest operation time.
If the shortest time is on the first machine, do the job first; if it is on the second
machine, do the job last. In the case of a tie, do the job on the first machine.
Repeat Steps 2 and 3 for each remaining job until the schedule is complete.
EXAMPLE 22.2: n Jobs on Two Machines
We can illustrate this procedure by scheduling four jobs through two machines.
SOLUTION
Step 1: List operation times.
Job
Operation Time
on Machine 1
Operation Time
on Machine 2
A
3
2
B
6
8
C
5
6
D
7
4
Steps 2 and 3: Select the shortest operation time and assign. Job A is shortest on Machine
2 and is assigned first and performed last. (Once assigned, Job A is no longer available to be
scheduled.)
Step 4: Repeat Steps 2 and 3 until completion of the schedule. Select the shortest operation time among the remaining jobs. Job D is second-shortest on Machine 2, so it is performed second to last. (Remember, Job A is last.) Now Jobs A and D are not available for
scheduling. Job C is the shortest on Machine 1 among the remaining jobs. Job C is performed first. Now only Job B is left with the shortest operation time on Machine 1. Thus,
according to Step 3, it is performed first among the remaining, or second overall. (Job C was
already scheduled first.)
In summary, the solution sequence is C → B → D → A and the flow time is 25 days, which
is a minimum. Also minimized are total idle time and mean idle time. The final schedule
appears in Exhibit 22.4.
These steps result in scheduling the jobs having the shortest time in the beginning and end
of the schedule. As a result, the concurrent operating time for the two machines is maximized,
thus minimizing the total operating time required to complete the jobs.
Workcenter Scheduling
ex hibit 22.4
Chapter 22
599
Optimal Schedule of Jobs Using Johnson’s Rule
Machine 1
Job C
Job B
Machine 2
Idle
Job C
0
5
Job D
Job B
11
Idle but available
for other work
Job A
Job D
19
Job A
23
25
Cumulative time in days
Johnson’s method has been extended to yield an optimal solution for the n/3 case. When
flow-shop scheduling problems larger than n/3 arise (and they generally do), analytical solution procedures leading to optimality are not available. The reason for this is that, even though
the jobs may arrive in static fashion at the first machine, the scheduling problem becomes
dynamic, and waiting lines start to form in front of machines downstream. At this point,
it becomes a multistage queuing problem, which is generally solved using simulation techniques such as those discussed in Chapter 10.
S c h e d u ling a S e t N um b e r o f Jo b s o n the Sam e Nu mb er
of Ma ch ine s
Some workcenters have enough of the right kinds of machines to start all jobs at the same
time. Here, the problem is not which job to do first, but rather which particular assignment of
individual jobs to individual machines will result in the best overall schedule. In such cases,
we can use the assignment method.
The assignment method is a special case of the transportation method of linear programming. It can be applied to situations where there are n supply sources and n demand uses
(such as five jobs on five machines) and the objective is to minimize or maximize some
measure of effectiveness. This technique is convenient in applications involving the allocation
of jobs to workcenters, people to jobs, and so on. The assignment method is appropriate in
solving problems that have the following characteristics:
1.
2.
3.
There are n “things” to be distributed to n “destinations.”
Each thing must be assigned to one and only one destination.
Only one criterion can be used (minimum cost, maximum profit, or minimum completion time, for example).
EXAMPLE 22.3: Assignment Method
Suppose that a scheduler has five jobs that can be performed on any of five machines (n = 5).
The cost of completing each job–machine combination is shown in Exhibit 22.5. The scheduler
would like to devise a minimum-cost assignment. (There are 5!, or 120, possible assignments.)
SOLUTION
This problem may be solved by the assignment method, which consists of four steps (note that
this also can be solved using the Excel Solver):
1. Subtract the smallest number in each row from itself and all other numbers in that row.
(There will then be at least one zero in each row.)
2. Subtract the smallest number in each column from all other numbers in that column.
(There will then be at least one zero in each column.)
Assignment method
A special case of the
transportation method of
linear programming that is
used to allocate a specific
number of jobs to the same
number of machines.
600
Supply and Demand Planning and Control
Section 4
Assignment Matrix Showing Machine Processing Costs for Each Job
exhibit 22.5
Machine
Job
A
B
C
D
E
I
$5
$6
$4
$8
$3
II
6
4
9
8
5
III
4
3
2
5
4
IV
7
2
4
5
3
V
3
6
4
5
5
3. Determine if the minimum number of lines required to cover each zero is equal to
n. If so, an optimal solution has been found, because job machine assignments must
be made at the zero entries, and this test proves that this is possible. If the minimum
number of lines required is less than n, go to Step 4.
4. Draw the least possible number of lines through all the zeros. (These may be the same lines
used in Step 3.) Subtract the smallest number not covered by lines from itself and all other
uncovered numbers, and add it to the number at each intersection of lines. Repeat Step 3.
For the example problem, the steps listed in Exhibit 22.6 would be followed.
Procedure to Solve an Assignment Matrix
exhibit 22.6
Step 2: Column reduction—the smallest
number is subtracted from each column.
Step 1: Row reduction—the smallest number
is subtracted from each row.
Machine
Machine
Job
A
B
C
D
E
Job
A
B
C
D
E
I
II
III
IV
V
2
2
2
5
0
3
0
1
0
3
1
5
0
2
1
5
4
3
3
2
0
1
2
1
2
I
II
III
IV
V
2
2
2
5
0
3
0
1
0
3
1
5
0
2
1
3
2
1
1
0
0
1
2
1
2
Step 3: Apply line test—the number of lines to
cover all zeros is 4; because 5 are required,
go to step 4.
Step 4: Subtract smallest uncovered number and
add to intersection of lines. Using lines drawn
in Step 3, smallest uncovered number is 1.
Machine
Machine
Job
A
B
C
D
E
Job
A
B
C
D
E
I
II
III
IV
V
2
2
2
5
0
3
0
1
0
3
1
5
0
2
1
3
2
1
1
0
0
1
2
1
2
I
II
III
IV
V
1
1
2
4
0
3
0
2
0
4
0
4
0
1
1
2
1
1
0
0
0
1
3
1
3
Optimal solution—by “line test.”
Optimal assignments and their costs.
Machine
Job
A
B
C
D
E
I
II
III
IV
V
1
1
2
4
0
3
0
2
0
4
0
4
0
1
1
2
1
1
0
0
0
1
3
1
3
Job I to Machine E
Job II to Machine B
Job III to Machine C
Job IV to Machine D
Job V to Machine A
Total cost
$3
4
2
5
3
$17
Workcenter Scheduling
Chapter 22
601
Note that even though there are two zeros in three rows and three columns, the solution
shown in Exhibit 22.6 is the only one possible for this problem because Job III must be
assigned to Machine C to meet the “assign to zero” requirement. Other problems may have
more than one optimal solution, depending, of course, on the costs involved.
The nonmathematical rationale of the assignment method is one of minimizing opportunity
costs. For example, if we decided to assign Job I to Machine A instead of to Machine E, we would
be sacrificing the opportunity to save $2 ($5 – $3). The assignment algorithm in effect performs
such comparisons for the entire set of alternative assignments by means of row and column reduction, as described in Steps 1 and 2. It makes similar comparisons in Step 4. Obviously, if assignments are made to zero cells, no opportunity cost, with respect to the entire matrix, occurs.
S c h e d u ling n J obs on m Ma ch in es
Complex workcenters are characterized by multiple machine centers processing a variety of
different jobs arriving at the machine centers intermittently throughout the day. If there are n
jobs to be processed on m machines and all jobs are processed on all machines, then there are
(n!)m alternative schedules for this job set. Because of the large number of schedules that exist
for even small workcenters, computer simulation (see Chapter 10) is the only practical way to
determine the relative merits of different priority rules in such situations.
W h i c h P r i o r i t y R u l e S h o u l d B e U s e d ? We believe that the needs of most
manufacturers are reasonably satisfied by a relatively simple priority scheme that embodies
the following principles:
1.
2.
It should be dynamic; that is, computed frequently during a job to reflect changing
conditions.
It should be based in one way or another on slack (the difference between the work
remaining to be done on a job and the time remaining to do it).
Current approaches used by companies combine simulation with human schedulers to create
schedules.
SHOP-FLOOR CONT ROL
Scheduling job priorities is just one aspect of shop-floor control (now often called­­production
activity control). The APICS Dictionary defines a shop-floor control system as
A system for utilizing data from the shop floor as well as data processing
files to maintain and communicate status information on shop orders and
workcenters.
The major functions of shop-floor control are
∙
∙
∙
∙
∙
∙
Assigning the priority of each shop order.
Maintaining work-in-process quantity information.
Conveying shop-order status information to the office.
Providing actual output data for capacity control purposes.
Providing quantity by location by shop order for WIP inventory and accounting purposes.
Measuring efficiency, utilization, and productivity of manpower and machines.
G an t t Cha r ts
Smaller job shops and individual departments of large ones employ the venerable Gantt chart
to help plan and track jobs. As described in Chapter 4, the Gantt chart is a type of bar chart
that plots tasks against time. Gantt charts are used for project planning and to coordinate a
LO 22–3
Apply scheduling
techniques to the
manufacturing shop floor.
Shop-floor (production
activity) control
A system for utilizing data
from the shop floor to
maintain and communicate
status information on shop
orders and workcenters.
602
Supply and Demand Planning and Control
Section 4
exhibit 22.7
Gantt Chart
Gantt Chart Symbols
Job
Monday
Tuesday
Wednesday
Thursday
Friday
A
B
C
Maintenance
Start of an activity
End of an activity
Schedule allowed activity time
Actual work progress
Point in time where chart is reviewed
Time set aside for nonproduction
activities; e.g., repairs, routine
maintenance, material outages
number of scheduled activities. The example in Exhibit 22.7 indicates that Job A is behind
schedule by about four hours, Job B is ahead of schedule, and Job C has been completed, after
a delayed start for equipment maintenance. Note that whether the job is ahead of schedule or
behind schedule is based on where it stands compared to where we are now. In Exhibit 22.7,
we are at the end of Wednesday, and Job A should have been completed. Job B has already
had some of Thursday’s work completed.
Tools of Sh o p -F lo o r Co n t ro l
The basic tools of shop-floor control are
1.
2.
3.
Input/output (I/O)
control
Work being released
into a workcenter should
never exceed the planned
work output. When the
input exceeds the output,
backlogs build up at the
workcenter that increase
the lead time.
The daily dispatch list, which tells the supervisor which jobs are to be run, their priority, and how long each will take. (See Exhibit 22.8A.)
Various status and exception reports, including
a. The anticipated delay report, made out by the shop planner once or twice a week
and reviewed by the chief shop planner to see if there are any serious delays that
could affect the master schedule. (See Exhibit 22.8B.)
b. Scrap reports.
c. Rework reports.
d. Performance summary reports giving the number and percentage of orders completed on schedule, the lateness of unfilled orders, the volume of output, and so on.
e. Shortage list.
An input/output control report, which is used by the supervisor to monitor the workload–capacity relationship for each workstation. (See Exhibit 22.8C.)
I n p u t / O u t p u t C o n t r o l Input/output (I/O) control is a major feature of a
manufacturing planning and control system. Its major precept is that the planned work input
to a workcenter should never exceed the planned work output. When the input exceeds the
output, backlogs build up at the workcenter, which in turn increases the lead time estimates
for jobs upstream. Moreover, when jobs pile up at the workcenter, congestion occurs,
processing becomes inefficient, and the flow of work to downstream workcenters becomes
sporadic. (The water flow analogy to shop capacity control in Exhibit 22.9 illustrates the
general phenomenon.) Exhibit 22.8C shows an I/O report for a downstream workcenter.
Looking first at the lower or output half of the report, we see that output is far below plan.
It would seem that a serious capacity problem exists for this workcenter. However, a look
at the input part of the plan makes it apparent that the serious capacity problem exists at an
upstream workcenter feeding this workcenter. The control process would entail finding the
cause of upstream problems and adjusting capacity and inputs accordingly. The basic solution
is simple: Either increase capacity at the bottleneck station or reduce the input to it. (Input
reduction at bottleneck workcenters, incidentally, is usually the first step recommended by
production control consultants when job shops get into trouble.)
D a t a I n t e g r i t y Shop-floor control systems in most modern plants are now computerized,
with job status information entered directly into a computer as the job enters and leaves a
Workcenter Scheduling
Chapter 22
Some Basic Tools of Shop-Floor Control
ex hibit 22.8
A. Dispatch List
Workcenter 1501—Day 205
Start date
Job #
Description
Run time
201
203
205
205
207
208
15131
15143
15145
15712
15340
15312
Shaft
Stud
Spindle
Spindle
Metering rod
Shaft
11.4
20.6
4.3
8.6
6.5
4.6
B. Anticipated Delay Report
Dept. 24 April 8
Part #
Sched. date
New
date
Cause of delay
17125
4/10
4/15
Fixture broke
13044
4/11
5/1
Out for plating—
plater on strike
17653
4/11
4/14
New part holes
don’t align
Action
Toolroom will return
on 4/15
New lot started
Engineering laying out
new jig
C. Input/Output Control Report
Workcenter 0162
Week ending
505
512
519
526
Planned input
210
210
210
210
Actual input
110
150
140
130
–100
–160
–230
–310
Planned output
210
210
210
210
Actual output
140
120
160
120
Cumulative deviation
–70
–160
–210
–300
Cumulative deviation
workcenter. Many plants have gone heavily into bar coding and optical scanners to speed
up the reporting process and to cut down on data entry errors. As you might guess, the key
problems in shop-floor control are data inaccuracy and lack of timeliness. When these occur,
data fed back to the overall planning system are wrong, and incorrect production decisions are
made. Typical results are excess inventory, stockout problems, or both; missed due dates; and
inaccuracies in job costing.
Of course, maintaining data integrity requires that a sound data-gathering system be in
place. More importantly, however, it requires adherence to the system by everybody interacting with it. Most firms recognize this, but maintaining what is variously referred to as
shop discipline, data integrity, or data responsibility is not always easy. And despite periodic
drives to publicize the importance of careful shop-floor reporting by creating data integrity
task forces, inaccuracies can still creep into the system in many ways: A line worker drops a
part under the workbench and pulls a replacement from stock without recording either transaction. An inventory clerk makes an error in a cycle count. A manufacturing engineer fails
to note a change in the routing of a part. A department supervisor decides to work jobs in a
different order than specified in the dispatch list.
603
604
Supply and Demand Planning and Control
Section 4
exhibit 22.9
Shop Capacity Control Load Flow
New
orders
Production
control
Open unreleased
orders
Input rate
Work in process
(load)
Manufacturing
lead time
Capacity
Output
completed orders
Pr inciples o f Wo rkcen ter Sch ed u lin g
Much of our discussion of workcenter scheduling systems can be summarized in the following principles:
1.
2.
3.
There is a direct equivalence between workflow and cash flow.
The effectiveness of any shop should be measured by speed of flow through the shop.
Schedule jobs as a string, with process steps back to back.
4. Once started, a job should not be
interrupted.
5. Speed of flow is most efficiently
achieved by focusing on bottleneck
workcenters and jobs.
6. Reschedule every day.
7. Obtain feedback each day on jobs
that are not completed at each
workcenter.
8. Match workcenter input information
to what the worker can actually do.
9. When seeking improvement in
output, look for incompatibility
between engineering design and
­process execution.
10. Certainty of standards, routings,
and so forth, is not possible in
a shop, but always work toward
An assembly line supervisor taking notes as he observes employees.
achieving it.
© Corbis Super RF/Alamy RF
Workcenter Scheduling
Chapter 22
605
PER SONNEL SCHEDUL ING IN SERVICES
The scheduling problem in most service organizations revolves around setting weekly, daily,
and hourly personnel schedules. In this section, we present a simple analytical approach for
developing such schedules.
Sc h e d u ling Da ily Wor k T ime s
LO 22–4
Analyze employee
schedules in the service
sector.
We now show how bank clearinghouses and back-office operations of large bank branches
establish daily work times. Basically, management wants to derive a staffing plan that
(1) requires the fewest workers to accomplish the daily workload and (2) minimizes the variance between actual and planned output.
In structuring the problem, bank management defines inputs (checks, statements, investment documents, and so forth) as products, which are routed through different processes or
functions (receiving, sorting, encoding, and so forth).
To solve the problem, a daily demand forecast is made by product for each function. This is
converted to labor hours required per function, which in turn is converted to workers required
OSCM AT WORK
Employee Scheduling Software Applied to
Security
ScheduleSource Inc. of Broomfield, Colorado, offers an
integrated suite of tools for workforce management named
TeamWork. At the heart of TeamWork is a customizable and
automated employee scheduling system. The benefits of
TeamWork software include features such as Web-based,
optimized schedules; zero conflict scheduling; time and
attendance recordkeeping; e-mail notifications; audit trails;
advanced reporting; and accessibility from anywhere anytime. The way it works is this:
Step 1: Define labor requirements.
McGraw-Hill Education, Inc
Step 2: Establish employee availability.
McGraw-Hill Education, Inc
Step 3: Assign employees to particular skill sets and rank
an employee’s skill set level from 1 to 10 (1 being novice, 5
being average, and 10 being superlative).
Step 4: The TeamWork software automatically builds a
schedule.
McGraw-Hill Education, Inc
ScheduleSource customers include the Transportation
Security Administration (TSA). ScheduleSource was successfully implemented to generate schedules for more than
44,000 federal airport security personnel at 429 airports.
Over 30,000,000 individual shifts were scheduled in the airport security deployment.
606
Supply and Demand Planning and Control
Section 4
per function. These figures are then tabulated, summed, and adjusted by an absence and vacation factor to give planned hours. They are then divided by the number of hours in the workday to yield the number of workers required. This yields the daily staff hours required. (See
Exhibit 22.10.) This becomes the basis for a departmental staffing plan that lists the workers
required, workers available, variance, and managerial action to deal with the variance. (See
Exhibit 22.11.)
S che dulin g Ho u rly Wo rk T imes
Services such as restaurants face changing requirements from hour to hour. More workers
are needed for peak hours, and fewer are needed in between. Management must continuously adjust to this changing requirement. This kind of personnel scheduling situation can
be approached by applying a simple rule, the “first-hour” principle. This procedure can be
best explained using the following example. Assume that each worker works continuously
for an eight-hour shift. The first-hour rule says that for the first hour, we assign a number
of workers equal to the requirement in that period. For each subsequent period, assign the
exact number of additional workers to meet the requirements. When in a period one or more
workers come to the end of their shifts, add more workers only if they are needed to meet the
requirement. The following table shows the worker requirements for the first 12 hours in a
24-hour restaurant:
Period
10 a.m. 11 a.m. Noon 1 p.m 2 p.m. 3 p.m. 4 p.m. 5 p.m. 6 p.m. 7 p.m. 8 p.m.
Requirement
exhibit 22.10
4
6
8
8
6
4
4
6
8
10
9 p.m.
10
6
Daily Staff Hours Required to Schedule Daily Work Times
Function
Receive
Product
Daily Volume
P/H
Checks
2,000
Statements
1,000
Preprocess
Microfilm
Verify
Totals
Hstd
P/H
Hstd
P/H
Hstd
P/H
Hstd
Hstd
1,000
2.0
600
3.3
240
8.3
640
3.1
16.8
—
—
600
1.7
250
4.0
150
6.7
12.3
200
2.0
150
2.7
16.7
300
1.7
60
8.4
11.7
77.5
Notes
200
30
6.7
15
13.3
Investments
400
100
4.0
50
8.0
Collections
500
300
1.7
—
20.0
Total hours required
14.3
26.3
16.0
20.8
Times 1.25 (absences
and vacations)
17.9
32.9
20.0
26.0
2.2
4.1
2.5
3.2
Divided by 8 hours
equals staff required
Note: P/H indicates production rate per hour; Hstd indicates required hours.
exhibit 22.11
Staffing Plan
Function
Staff Required
Staff Available
Variance (±)
Receive
2.3
2.0
−0.3
Management Actions
Use overtime.
Preprocess
4.1
4.0
−0.1
Use overtime.
Microfilm
2.5
3.0
+0.5
Use excess to verify.
Verify
3.3
3.0
−0.3
Get 0.3 from microfilm.
12.1
Workcenter Scheduling
Chapter 22
607
The schedule shows that four workers are assigned at 10 A.M., two are added at 11 A.M., and
another two are added at noon to meet the requirement. From noon to 5 P.M. we have eight
workers on duty. Note the overstaffing between 2 P.M. and 6 P.M. The four workers assigned at
10 A.M. finish their eight-hour shifts by 6 P.M., and four more workers are added to start their
shifts. The two workers starting at 11 A.M. leave by 7 P.M., and the number of workers available
drops to six. Therefore, four new workers are assigned at 7 P.M. At 9 P.M., there are 10 workers
on duty, which is more than the requirement, so no worker is added. This procedure continues
as new requirements are given.
Period
10 a.m. 11 a.m. Noon 1 p.m. 2 p.m. 3 p.m. 4 p.m. 5 p.m. 6 p.m. 7 p.m. 8 p.m. 9 p.m.
Requirement
4
6
8
8
6
4
4
6
8
10
10
6
Assigned
4
2
2
0
0
0
0
0
4
4
2
0
On duty
4
6
8
8
8
8
8
8
8
10
10
10
Another option is splitting shifts. For example, the worker can come in, work for four
hours, then come back two hours later for another four hours. The impact of this option in
scheduling is essentially similar to that of changing the lot size in production. When workers
start working, they have to log in, change uniforms, and probably get necessary information
from workers in the previous shift. This preparation can be considered as the “setup cost” in a
production scenario. Splitting shifts is like having smaller production lot sizes and thus more
preparation (more setups). This is a complex problem that can be solved by specialized linear
programming methods.
Concept Connections
LO 22–1 Explain workcenter scheduling.
Summary
∙ A schedule is a timetable for performing work that
indicates how resources are to be used over time.
∙ This chapter focuses on short-term schedules showing
what is to be done over the next few days or weeks.
∙ One characteristic of a scheduling system is whether
capacity is directly considered or not (finite versus
infinite loading). Another characteristic is whether
jobs are scheduled forward, from now and into the
future, or backward from a due date.
∙ Typically, either labor or equipment is scheduled,
depending on what is the most limiting resource in a
process.
∙ Typically, work is done in workcenters and the main
focus of the chapter is on scheduling jobs through
these areas. This process involves (1) allocating jobs
to resources, (2) sequencing the jobs at each resource,
(3) releasing (dispatching) the jobs, and (4) monitoring the status of the jobs.
∙ Jobs are often sequenced (ordered) using priority
rules based on processing time, due dates, or order of
arrival. This entire process is often done using a comprehensive software package known as a manufacturing execution system.
Key Terms
Manufacturing Execution System (MES) An information
system that schedules, dispatches, tracks, monitors, and
controls production on the factory floor.
Workcenter Often referred to as a job shop, a process structure suited for low-volume production of a
great variety of nonstandard products. Workcenters
sometimes are referred to as departments and are
focused on a particular type of operation.
Infinite loading Work is assigned to a workcenter based
on what is needed over time. Capacity is not considered.
Finite loading Each resource is scheduled in detail
using the setup and run time required for each order. The
608
Section 4
Supply and Demand Planning and Control
system determines exactly what will be done by each
resource at every moment during the working day.
Forward scheduling Schedules from now into the future
to tell the earliest that an order can be completed.
Backward scheduling Starts from some date in the
future (typically the due date) and schedules the required
operations in reverse sequence. Tells the latest time
when an order can be started so that it is completed by a
specific date.
Machine-limited process Equipment is the critical
resource that is scheduled.
Labor-limited process People are the key resource that
is scheduled.
Dispatching The activity of initiating scheduled work.
Sequencing The process of determining which job to
start first on a machine or workcenter.
Priority rules The logic used to determine the sequence
of jobs in a queue.
LO 22–2 Analyze scheduling problems using priority rules and more specialized techniques.
Summary
∙ Many different techniques are available for scheduling
jobs. Three of the most common approaches are analyzed in this section.
∙ Priority rules are used when there are a number of
jobs that need to be run on a single machine.
∙ A special case is when a set of jobs needs to be run
on only two machines. In this case, a technique called
“Johnson’s rule” can be used to minimize the time to
complete all jobs.
∙ Another special case is when there are exactly the
same number of jobs as machines available, and the
jobs each need to be assigned to a unique machine (not
all of the machines are equally efficient). In this case,
the assignment method can be used.
∙ These different techniques are mixed and matched to
real-world scheduling situations.
Key Terms
Johnson’s rule A sequencing rule used for schedul-
ing any number of jobs on two machines. The rule is
designed to minimize the time required to complete all
the jobs.
Assignment method A special case of the transporta-
tion method of linear programming that is used to allocate a specific number of jobs to the same number of
machines.
LO 22–3 Apply scheduling techniques to the manufacturing shop floor.
Summary
∙ The job of actually managing work in a manufacturing
environment is called shop-floor or production activity control.
∙ The system consists of computer-based tracking and
decision support, augmented with visual charts and
lists to quickly convey information to workers.
∙ An important feature of the system is acquiring the
ability to manage the inflow of work so the system
is not overloaded. This is called input/output control,
and recognizes that production systems have limited
capacity.
Key Terms
Shop-floor (production activity) control A system
for utilizing data from the shop floor to maintain and
communicate status information on shop orders and
workcenters.
Input/output (I/O) control Work being released into a
workcenter should never exceed the planned work output. When the input exceeds the output, backlogs build
up at the workcenter that increase the lead time.
Workcenter Scheduling
609
Chapter 22
LO 22–4 Analyze employee schedules in the service sector.
Summary
∙ Service sector scheduling focuses on setting detailed personnel schedules. It answers the questions of when and
where each employee will be working in the short term.
∙ These techniques are driven by daily worker requirements that may vary considerably by hour and day.
Solved Problems
LO 22–2
SOLVED PROBLEM 1
Consider the following data on jobs waiting to be processed on a single machine in a job shop.
They are listed here in order of their arrival at the machine:
Job
Processing
Time (days)
Due Date
(days hence)
A
5
B
3
5
C
4
12
D
7
14
E
2
11
8
Develop a schedule for these jobs based on the following rules: FCFS, SOT, and EDD. In
each schedule, list the flow time and lateness for each job (the lateness of a job that is done
early equals zero), as well as the mean for each measure.
Solution
FCFS Schedule
Job
Sequence
Processing
Time (days)
Due Date
(days hence)
Flow
Time (days)
Lateness
(days)
A
5
8
0+5= 5
5− 8= 0
B
3
5
5+3= 8
8− 5= 3
12 − 12 = 0
C
4
12
8 + 4 = 12
D
7
14
12 + 7 = 19
19 − 14 = 5
E
2
11
19 + 2 = 21
21 − 11 = 10
5 + 8 + 12 + 19 + 21
​Average flow time = _________________
​
​ = 13.0​
5
0 + 3 + 0 + 5 + 10
​Average flow time = _________________
​
​ = 3.6​
5
SOT Schedule
Job
Sequence
Processing
Time (days)
Due Date
(days hence)
Flow
Time (days)
E
2
11
0+2= 2
Lateness
(days)
2 − 11 = 0
B
3
5
2+3= 5
5− 5=0
C
4
12
5+4= 9
9 − 12 = 0
A
5
8
9 + 5 = 14
14 − 8 = 6
D
7
14
14 + 7 = 21
21 − 14 = 7
2 + 5 + 9 + 14 + 21
​Average flow time = __________________
​
​ = 10.2​
5
0+0+0+6+7
​Average flow time = ________________
​
​ = 2.6​
5
610
Supply and Demand Planning and Control
Section 4
EDD Schedule
Job
Sequence
Processing
Time (days)
Due Date
(days hence)
Flow
Time (days)
Lateness
(days)
B
3
5
0+3= 3
A
5
8
3+5= 8
3− 5=0
8− 8=0
E
2
11
8 + 2 = 10
10 − 11 = 0
C
4
12
10 + 4 = 14
14 − 12 = 2
D
7
14
14 + 7 = 21
21 − 14 = 7
3 + 8 + 10 + 14 + 21
​Average flow time = ____________________
​
​ = 11.2​
5
0+0+0+2+7
​Average flow time = ________________
​
​ = 1.8​
5
SOLVED PROBLEM 2
Joe’s Auto Seat Cover and Paint Shop is bidding on a contract to do all the custom work for
Smiling Ed’s used car dealership. One of the main requirements in obtaining this contract is
rapid delivery time, because Ed—for reasons we shall not go into here—wants the cars facelifted and back on his lot in a hurry. Ed has said that if Joe can refit and repaint five cars that
Ed has just received in 24 hours or less, the contract will be his. The following is the time (in
hours) required in the refitting shop and the paint shop for each of the five cars. Assuming
that cars go through the refitting operations before they are repainted, can Joe meet the time
requirements and get the contract?
Car
Refitting
Time (hours)
Repainting
Time (hours)
A
6
3
B
0
4
C
5
2
D
8
6
E
2
1
Solution
This problem can be viewed as a two-machine flow shop and can be easily solved using
­Johnson’s rule. The final schedule is B–D–A–C–E.
Manually, the problem is solved as follows:
Original Data
Johnson’s Rule
Car
Refitting
Time (hours)
Repainting
Time (hours)
Order
of Selection
Position
in Sequence
A
6
3
4
3
B
0
4
1
1
C
5
2
3
4
D
8
6
5
2
E
2
1
2
5
0
8
Refit
Repaint
D
14
19
A
B
D
C
21
E
A
C
E
8
4
14
17
21 22
Workcenter Scheduling
Chapter 22
611
SOLVED PROBLEM 3
The production scheduler for Marion Machine Shop has six jobs ready to be processed that
can each be assigned to any of six different workstations. Due to the characteristics of each
job and the different equipment and skills at the workstations, the time to complete a job
depends on the station it is assigned to. The following is data on the jobs and the time it would
take to do each job at each workstation.
Job Completion Time at Workstation (hours)
Job
1
2
3
A
3.2
3.5
2.9
3
4
4
5
3.6
6
B
2.7
2.9
2.3
3
3.1
3.7
C
3.8
4
4.3
4.5
4.1
3.6
D
2.8
2.1
2.9
2.5
3
2.2
E
6.1
6.5
6.7
7
6
6.2
F
1.5
1.3
1.9
2.9
4
3.6
Assign each job to a machine in order to minimize total processing time.
Solution
Use the assignment method following Example 22.3.
a. Subtract the smallest number in each row from itself and all other numbers in that row.
Job Completion Time at Workstation (hours)
Job
1
2
4
5
6
A
0.3
0.6
0
3
0.1
1.1
0.7
B
0.4
0.6
0
0.7
0.8
1.4
C
0.2
0.4
0.7
0.9
0.5
0
D
0.7
0
0.8
0.4
0.9
0.1
E
0.1
0.5
0.7
1
0
0.2
F
0.2
0
0.6
1.6
2.7
2.3
b. Subtract the smallest number in each column from itself and all other numbers in that
column.
Job Completion Time at Workstation (hours)
Job
1
2
3
4
5
6
A
0.2
0.6
0
0
1.1
0.7
B
0.3
0.6
0
0.6
0.8
1.4
C
0.1
0.4
0.7
0.8
0.5
0
D
0.6
0
0.8
0.3
0.9
0.1
E
0
0.5
0.7
0.9
0
0.2
F
0.1
0
0.6
1.5
2.7
2.3
c. Determine the minimum number of lines required to cover each zero.
Job Completion Time at Workstation (hours)
Job
1
2
3
4
5
6
A
0.2
0.6
0
0
1.1
0.7
B
0.3
0.6
0
0.6
0.8
1.4
C
0.1
0.4
0.7
0.8
0.5
0
D
0.6
0
0.8
0.3
0.9
0.1
E
0
0.5
0.7
0.9
0
0.2
F
0.1
0
0.6
1.5
2.7
2.3
612
Section 4
Supply and Demand Planning and Control
d. We can cover every zero with just five lines. Subtract the smallest number not covered
by lines (0.1) from itself and every other uncovered number, and add it to the number
at each intersection of lines. Repeat part (c).
Job Completion Time at Workstation (hours)
Job
1
2
3
5
6
A
0.2
0.7
0.1
0
4
1.1
0.8
B
0.2
0.6
0
0.5
0.7
1.4
C
0
0.4
0.7
0.7
0.4
0
D
0.5
0
0.8
0.2
0.8
0.1
E
0
0.6
0.8
0.9
0
0.3
F
0
0
0.6
1.4
2.6
2.3
e. It now takes six lines to cover all zeroes. Make job assignments at zero entries, starting
with those jobs that have just one zero entry. Then, move to jobs that have more than
one zero entry, but only one zero remaining that has not been assigned to another job
yet, and so on. The job assignments and times are as follows:
Job
Machine
A
4
3.0
B
3
2.3
D
2
2.1
F
1
1.5
C
6
3.6
E
LO 22–4
Time
5
6.0
Total:
18.5
SOLVED PROBLEM 4
Albert’s Downtown Café is a very popular restaurant in Indianapolis that serves breakfast,
lunch, and dinner six days a week. The restaurant needs its wait staff in varying numbers
throughout the day to serve customers. Analysis of past data indicates that Albert has the following staffing needs throughout the day.
6:00 7:00 8:00 9:00 10:00 11:00 Noon 1:00 2:00 3:00 4:00 5:00
Servers
needed
3
6
5
3
2
4
7
5
3
3
4
6
6:00 7:00 8:00 9:00
7
7
4
2
Currently, servers work 8-hour shifts. They eat when they can so there are no scheduled lunch
hours.
a. Use the first-hour principle to develop a schedule showing how many workers start
a shift in each hour, how many servers are on duty each hour, and how many excess
servers are on duty each hour. Comment on your results.
b. Albert has noticed that during slow periods he often has far too many servers on duty.
Also, the wait staff has been complaining about the long hours in the current policy.
Therefore, Albert is considering shortening the shifts to either 6 hours or 4 hours. The
current wait staff would prefer 6-hour shifts. Using the first-hour principle, develop
schedules based on both 6-hour and 4-hour shifts. Comment on each.
c. Assume that servers at Albert’s are paid $7.50 per hour. Cost out each of the schedules
you have developed and compare the costs.
Workcenter Scheduling
613
Chapter 22
Solution
a.
6:00 7:00 8:00 9:00 10:00 11:00 Noon 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00
Servers
needed
3
6
5
3
2
4
7
5
3
3
4
6
7
7
4
2
Start shift
3
3
0
0
0
0
1
0
0
2
1
2
1
0
0
0
Off shift
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
On duty
3
6
6
6
6
6
7
7
4
3
4
6
7
7
6
6
Excess
staff
0
0
1
3
4
2
0
2
1
0
0
0
0
0
2
4
b.
There is an excess of staff during the morning lull and at the end of the workday. Due
to the 8-hour shifts, the early morning staff end their shifts during the afternoon lull,
so that the slow period is fairly well staffed. You should also note that the workers
who start at 3:00 P.M. and later will not be able to finish their 8-hour shift by the 10:00
P.M. closing time. Obviously, using only 8-hour shifts is not practical for the evenings.
6-Hour Shifts
6:00 7:00 8:00 9:00 10:00 11:00 Noon 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00
Servers
needed
3
6
5
3
2
4
7
5
3
3
4
6
7
7
4
2
Start shift
3
3
0
0
0
0
4
1
0
0
0
1
5
1
0
0
Off shift
0
0
0
0
0
0
3
3
0
0
0
0
4
1
0
0
On duty
3
6
6
6
6
6
7
5
5
5
5
6
7
7
7
7
Excess
staff
0
0
1
3
4
2
0
0
2
2
1
0
0
0
3
5
Again we’re bringing on people at the end of the day that will not be able to finish out their
full shift. We haven’t seemed to improve on the excess staff much, if at all, here either.
4-Hour Shifts
6:00 7:00 8:00 9:00 10:00 11:00 Noon 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00
Servers
needed
3
6
5
3
2
4
7
5
3
3
4
6
7
7
4
2
Start shift
3
3
0
0
0
4
3
0
0
0
4
2
1
0
1
0
Off shift
0
0
0
0
3
3
0
0
0
4
3
0
0
0
4
2
On duty
3
6
6
6
3
4
7
7
7
3
4
6
7
7
4
2
Excess
staff
0
0
1
3
1
0
0
2
4
0
0
0
0
0
0
0
This schedule seems to do a much better job matching staff to needs, and we only start
one employee too late to finish the 4-hour shift.
c. In costing out the schedules, simply sum the numbers on duty each hour throughout
the day and multiply by $7.50.
Schedule
Worker-Hours
Cost
8-hour
90
$675.00
6-hour
94
705.00
4-hour
82
615.00
614
Supply and Demand Planning and Control
Section 4
Because the 4-hour shift policy better matches servers to demand, it has the lower
daily labor cost. This policy will require us to have the largest number of employees,
though, so Albert will have to do some hiring. He should also consider the impact on
morale of current employees if he cuts their hours in half. They would like a 6-hour
shift policy, but given the restaurant’s demand patterns, and using the first-hour scheduling principle, that would result in the least efficient schedule.
Clearly, scheduling workers in a service business is not a simple task! There are
costs as well as human issues to consider. For Albert, the best solution will likely contain a mix of different length shifts—ideally, he’ll be able to match employees with
shifts they will be happy with.
Discussion Questions
LO22–1
LO22–2
1.
2.
3.
4.
5.
6.
7.
8.
LO22–3
LO22–4
9.
10.
11.
12.
13.
14.
15.
What are the objectives of workcenter scheduling?
Distinguish between a workcenter, a GT cell, and an assembly line.
What practical considerations are deterrents to using the SOT rule?
What priority rule do you use in scheduling your study time for midterm examinations?
If you have five exams to study for, how many alternative schedules exist?
The SOT rule provides an optimal solution in a number of evaluation criteria. Should the
manager of a bank use the SOT rule as a priority rule? Why?
Why does batching cause so much trouble in workcenters?
What job characteristics would lead you to schedule jobs according to “longest processing time first”?
Why is managing bottlenecks so important in workcenter scheduling?
Under what conditions is the assignment method appropriate?
The chapter discusses the use of Gantt charts in shop floor control. You were introduced
to Gantt charts in Chapter 4, “Project Management.” Projects and workcenter processes
are rather different in nature. Why is it that the same tool can be used in both projects and
workcenters?
Why is it desired to have smooth, continuous flow on the shop floor?
Data integrity is a big deal in industry. Why?
Explain why scheduling personnel in a service operation can be challenging.
How might planning for a special customer affect the personnel schedule in a service?
Objective Questions
LO22–1
LO22–2
1. What is the term used for an information system that links, schedules, dispatches, tracks,
monitors, and controls customer encounters with a service organization?
2. What do we generally call an area in a business where productive resources are organized
and work is completed?
3. What type of inventory are we trying to minimize as the result of workcenter scheduling?
4. A key part of workcenter scheduling is job sequencing—deciding in what order jobs are
scheduled to start/complete. What is the term for the simple rules used to aid this process
using a single piece of data about the jobs?
5. The following table gives the operation times and due dates for five jobs that are to be
processed on a machine. Assign the jobs according to the shortest operation time and
calculate the mean flow time. (Answer in Appendix D)
Workcenter Scheduling
Job
Processing
Time
Due Date
(Days Hence)
101
6 days
5
102
7 days
3
103
4 days
4
104
9 days
7
105
5 days
2
Chapter 22
615
6. The MediQuick lab has three lab technicians available to process blood samples and three
jobs that need to be assigned. Each technician can do only one job. The following table
represents the lab’s estimate (in dollars) of what it will cost for each job to be completed.
Assign the technicians to the jobs to minimize costs.
Job
Tech A
Tech B
Tech C
J-432
11
14
6
J-487
8
10
11
J-492
9
12
7
7. Christine has three cars that must be overhauled by her ace mechanic, Megan. Given the
following data about the cars, use the least slack per remaining operation to determine
Megan’s scheduling priority for each car. (Answer in Appendix D)
Car
Customer Pick-Up
Time (hours hence)
Remaining Overhaul
Time (hours)
Remaining
Operation
A
10
4
Painting
B
17
5
Wheel alignment, painting
C
15
1
Chrome plating, painting, seat repair
8. The following list of jobs in a critical department includes estimates of their required times.
Job
Required
T (days)
Days to
Delivery Promise
Slack
A
8
12
4
B
3
9
6
C
7
8
1
D
1
E
10
F
6
G
5
H
4
11
−10 (late)
10
−8 (late)
6
10
−20
4
−13
2
a. Use the shortest operation time rule to schedule these jobs.
What is the schedule?
What is the mean flow time?
b. The boss does not like the schedule in part (a). Jobs E and G must be done first, for
obvious reasons. (They are already late.) Reschedule and do the best you can while
scheduling Jobs E and G first and second, respectively.
What is the new schedule?
What is the new mean flow time?
9. A manufacturing facility has five jobs to be scheduled into production. The following
table gives the processing times plus the necessary wait times and other necessary delays
616
Supply and Demand Planning and Control
Section 4
for each of the jobs. Assume that today is April 3, that the facility will work every day
between now and the due dates, and the jobs are due on the dates shown:
Job
Days of Actual
Processing
Time Required
Days of
Necessary
Delay Time
Total Time
Required
Date Job
Due
1
2
12
14
April 30
2
5
8
13
April 21
3
9
15
24
April 28
4
7
9
16
April 29
5
4
22
26
April 27
Determine two schedules, stating the order in which the jobs are to be done. Use the
critical ratio priority rule for one. You may use any other rule for the second schedule as
long as you state what it is. (Answer in Appendix D)
10.
The following table contains information regarding jobs that are to be scheduled through
one machine.
Job
Processing
Time
Due
Date
A
4
20
B
12
30
C
2
15
D
11
16
E
10
18
F
3
5
G
6
9
a. What is the first-come, first-served (FCFS) schedule?
b. What is the shortest operating time (SOT) schedule?
c. What is the slack time remaining (STR) schedule?
d. What is the earliest due date (EDD) schedule?
e. What are the mean flow times for each of the schedules above?
11. Bill Edstrom, managing partner at a biomedical consulting firm, has requested your
expert advice in devising the best schedule for the following consulting projects, starting
on February 2.
Description of Consultation
Call Received
Task
Length
Company
Date
I
3 days
Novartis Corp.
February 1
Time
Due Date
(close of business)
9 a.m.
February 5
II
1 day
Reardon Biotech Corp.
February 1
10 a.m.
February 6
III
2 days
Vertex Pharmaceuticals
February 1
11 a.m.
February 8
IV
2 days
OSI Pharmaceuticals
February 1
1 p.m.
February 7
The consulting firm charges a flat rate of $4,000 per day. All four firms impose fines for
lateness. Reardon Biotech charges a $500-per-day fine for each day that the completion of the
consulting work is past the due date; Vertex Pharmaceuticals, Novartis, and OSI Pharmaceuticals all charge a fine of $1,500 per day for each day late.
Prepare alternative schedules based on the following priority rules: SOT, FCFS, EDD,
STR, and another rule—longest processing time (LPT), which orders jobs according to longest assigned first, second-longest assigned second, and so on. For the sake of simplicity,
assume that consulting work is performed seven days a week. Which rule provides Bill with
the best schedule? Why?
Workcenter Scheduling
Chapter 22
617
12. Seven jobs must be processed in two operations: A and B. All seven jobs must go
through A and B in that sequence—A first, then B. Determine the optimal order (shortest flow time to complete all the jobs) in which the jobs should be sequenced through
the process using these times:
Job
Process A Time
Process B Time
1
9
6
2
8
5
3
7
7
4
6
3
5
1
2
6
2
6
7
4
7
13. Jobs A, B, C, D, and E must go through Processes I and II in that sequence (Process I
first, then Process II). Use Johnson’s rule to determine the optimal sequence in which to
schedule the jobs to minimize the total required time.
Job
Required
Processing
Time on I
Required
Processing
Time on II
A
4
5
B
16
14
C
8
7
D
12
11
E
3
9
14. Joe is the production scheduler in a brand-new custom refinishing auto service shop
located near the border. This system is capable of handling 10 cars per day. The sequence
is customizing first, followed by repainting.
Car
Customizing
Time (hours)
Painting
(hours)
Customizing
Time (hours)
Painting
(hours)
1
3.0
1.2
6
2.1
0.8
2
2.0
3
2.5
0.9
7
3.2
1.4
1.3
8
0.6
1.8
4
0.7
5
1.6
0.5
9
1.1
1.5
1.7
10
1.8
0.7
Car
In what sequence should Joe schedule the cars to minimize the time needed to complete all the cars?
15. Schedule the following six jobs through two machines in sequence to minimize the flow
time using Johnson’s rule.
Operations Time
Job
Machine 1
Machine 2
A
5
2
B
16
15
C
1
9
D
13
11
E
17
3
F
18
7
618
Supply and Demand Planning and Control
Section 4
16. The following matrix shows the costs in thousands of dollars for assigning Individuals A, B,
C, and D to Jobs 1, 2, 3, and 4. Solve the problem showing your final assignments in order
to minimize cost. Assume that each job will be assigned to one individual.
Jobs
Individuals
1
2
3
4
A
7
9
3
5
B
3
11
7
6
C
4
5
6
2
D
5
9
10
12
17. In a workcenter, six machinists were uniquely qualified to operate any one of the five
machines in the shop. The workcenter had considerable backlog, and all five machines were
kept busy at all times. The one machinist not operating a machine was usually occupied
doing clerical or routine maintenance work. Given the following value schedule for each
machinist on each of the five machines, develop the optimal assignments. Assume only one
machinist will be assigned to each machine. (Hint: Add a dummy column with zero cost
values, and solve using the assignment method.)
Machine
Machinist
1
2
3
4
5
A
65
B
30
50
60
55
80
75
125
50
C
40
75
35
85
95
45
D
60
40
115
130
110
E
90
85
40
80
95
F
145
60
55
45
85
18. Joe has achieved a position of some power in the institution in which he currently resides
and works. In fact, things have gone so well that he has decided to divide the day-to-day
operations of his business activities among four trusted subordinates: Big Bob, Dirty Dave,
Baby Face Nick, and Tricky Dick. The question is how he should do this in order to take
advantage of his associates’ unique skills and to minimize the costs from running all areas
for the next year. The following matrix summarizes the costs that arise under each possible
combination of men and areas.
Area
Associate
Big Bob
1
2
3
4
$1,400
$1,800
$ 700
$1,000
Dirty Dave
600
2,200
1,500
1,300
Baby Face Nick
800
1,100
1,200
500
1,000
1,800
2,100
1,500
Tricky Dick
19. The following matrix contains the costs (in dollars) associated with assigning Jobs A, B, C,
D, and E to Machines 1, 2, 3, 4, and 5. Assign jobs to machines to minimize costs.
Machines
Jobs
1
2
3
A
6
11
12
3
10
B
5
12
10
7
9
C
7
14
13
8
12
D
4
15
16
7
9
13
17
11
12
E
4
5
Final PDF to printer
Workcenter Scheduling
LO 22–3
LO 22–4
619
Chapter 22
20. What is another common term for shop-floor control?
21. Which graphical tool commonly used in project management is also very useful in
shop-floor control?
22. What shop-floor control document tells the supervisor which jobs are to be run, in what
order, and how long each will take?
23. What feature of manufacturing planning and control systems operates under the premise that the planned work input to a workcenter should never exceed the planned work
output?
24. A hotel has to schedule its receptionists according to hourly loads. Management has
identified the number of receptionists needed to meet the hourly requirement, which
changes from day to day. Assume each receptionist works a four-hour shift. Given the
following staffing requirement in a certain day, use the first-hour principle to find the
personnel schedule:
Period
8 a.m. 9 a.m. 10 a.m. 11 a.m. Noon 1 p.m. 2 p.m. 3 p.m. 4 p.m. 5 p.m. 6 p.m. 7 p.m.
Requirement
2
3
5
8
8
6
5
8
8
6
4
3
Assigned
On duty
25. The following wait staff members are needed at a restaurant. Use the first-hour principle to generate a personnel schedule. Assume a four-hour shift.
Period
11 a.m. Noon 1 p.m. 2 p.m. 3 p.m. 4 p.m. 5 p.m. 6 p.m. 7 p.m. 8 p.m. 9 p.m.
Requirements
4
8
5
3
2
3
5
7
5
4
2
Assigned
On duty
26. Which simple scheduling concept can be applied to help schedule workers for a service
operation with changing staffing requirements throughout the day?
Case: Keep Patients Waiting? Not in My Office
Good doctor–patient relations begin with both parties
being punctual for appointments. I am Dr. Schafer, and
being punctual is particularly important in my specialty:
pediatrics. Mothers whose children have only minor
problems don’t like them to sit in the waiting room with
really sick ones, and the sick kids become fussy if they
have to wait long.
But lateness—no matter who’s responsible for it—can
cause problems in any practice. Once you’ve fallen more than
slightly behind, it may be impossible to catch up that day.
And although it’s unfair to keep someone waiting who may
have other appointments, the average office patient cools his
heels for almost 20 minutes, according to one recent survey.
Patients may tolerate this, but they don’t like it.
I don’t tolerate that in my office, and I don’t believe
you have to in yours. I see patients exactly at the appointed
hour more than 99 times out of 100. So there are many
GPs (grateful patients) in my busy solo practice. Parents
often remark to me, “We really appreciate your being on
time. Why can’t other doctors do that, too?” My answer
is “I don’t know, but I’m willing to tell them how I do it.”
Booking Appointments Realistically
The key to successful scheduling is to allot the proper
amount of time for each visit, depending on the services
required, and then stick to it. This means that the physician must pace her- or himself carefully, receptionists
must be corrected if they stray from the plan, and patients
must be taught to respect their appointment times.
By actually timing a number of patient visits, I found
that they break down into several categories. We allow half
an hour for any new patient, 15 minutes for a well-baby
checkup or an important illness, and either 5 or 10 minutes
for a recheck on an illness or injury, an immunization, or
a minor problem like warts. You can, of course, work out
your own time allocations, geared to the way you practice.
Source: W. B. Schafer, “Keep Patients Waiting? Not in My Office,” Medical Economics, May 12, 1986, pp. 137–41. Copyright © by Medical Economics. Reprinted
by permission. Medical Economics is a copyrighted publication of Advanstar Communications, Inc. All rights reserved.
jac66107_ch22_590-621.indd
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01/10/17 12:30 PM
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Supply and Demand Planning and Control
When appointments are made, every patient is given
a specific time, such as 10:30 or 2:40. It’s an absolute
no-no for anyone in my office to say to a patient, “Come
in 10 minutes” or “Come in a half-hour.” People often
interpret such instructions differently, and nobody knows
just when they’ll arrive.
There are three examining rooms that I use routinely,
a fourth that I reserve for teenagers, and a fifth for emergencies. With that many rooms, I don’t waste time waiting for patients, and they rarely have to sit in the reception
area. In fact, some of the younger children complain that
they don’t get time to play with the toys and puzzles in
the waiting room before being examined, and their mothers have to let them play awhile on the way out.
On a light day, I see 20 to 30 patients between 9 A.M.
and 5 P.M. But our appointment system is flexible enough
to let me see 40 to 50 patients in the same number of
hours if I have to. Here’s how we tighten the schedule:
My two assistants (three on the busiest days) have standing orders to keep a number of slots open throughout each
day for patients with acute illnesses. We try to reserve more
such openings in the winter months and on the days following weekends and holidays, when we’re busier than usual.
Initial visits, for which we allow 30 minutes, are always
scheduled on the hour or the half-hour. If I finish such
a visit sooner than planned, we may be able to squeeze
in a patient who needs to be seen immediately. And, if
necessary, we can book two or three visits in 15 minutes
between well-checks. With these cushions to fall back on,
I’m free to spend an extra 10 minutes or so on a serious
case, knowing that the lost time can be made up quickly.
Parents of new patients are asked to arrive in the office
a few minutes before they’re scheduled in order to get the
preliminary paperwork done. At that time, the receptionist informs them, “The doctor always keeps an accurate
appointment schedule.” Some already know this and have
chosen me for that very reason. Others, however, don’t
even know that there are doctors who honor appointment
times, so we feel it’s best to warn them on the first visit.
a delay has been adjusted for, I’m on time for all later
appointments. The only situation I can imagine that
would really wreck my schedule is simultaneous emergencies in the office and at the hospital—but that has
never occurred.
When I return to the patient I’ve left, I say, “Sorry
to have kept you waiting, I had an emergency—a bad
cut” (or whatever). A typical reply from the parent: “No
problem, Doctor. In all the years I’ve been coming here,
you’ve never made me wait before. And I’d surely want
you to leave the room if my kid were hurt.”
Emergencies aside, I get few walk-ins, because it’s
generally known in the community that I see patients
only by appointment except in urgent circumstances. A
nonemergency walk-in is handled as a phone call would
be. The receptionist asks whether the visitor wants advice
or an appointment. If the latter, he or she is offered the
earliest time available for nonacute cases.
Fitting in Emergencies
Dealing with Latecomers
Emergencies are the excuse doctors most often give for
failing to stick to their appointment schedules. Well,
when a child comes in with a broken arm or the hospital calls with an emergency Caesarean section, naturally
I drop everything else. If the interruption is brief, I may
just scramble to catch up. If it’s likely to be longer, the
next few patients are given the choice of waiting or making new appointments. Occasionally, my assistants have
to reschedule all appointments for the next hour or two.
Most such interruptions, though, take no more than 10 to
20 minutes, and the patients usually choose to wait. I then
try to fit them into the spaces we’ve reserved for acute
cases that require last-minute appointments.
The important thing is that emergencies are never
allowed to spoil my schedule for the whole day. Once
Taming the Telephone
Phone calls from patients can sabotage an appointment
schedule if you let them. I don’t. Unlike some pediatricians, I don’t have a regular telephone hour, but my assistants will handle calls from parents at any time during
office hours. If the question is a simple one, such as “How
much aspirin do you give a one-year-old?” the assistant
will answer it. If the question requires an answer from me,
the assistant writes it in the patient’s chart and brings it to
me while I’m seeing another child. I write the answer in—
or she enters it in the chart. Then, she relays it to the caller.
What if the caller insists on talking with me directly?
The standard reply is “The doctor will talk with you personally if it won’t take more than one minute. Otherwise,
you’ll have to make an appointment and come in.” I’m
rarely called to the phone in such cases, but if the mother
is very upset, I prefer to talk with her. I don’t always limit
her to one minute; I may let the conversation run two or
three. But the caller knows I’ve left a patient to talk with
her, so she tends to keep it brief.
Some people are habitually late; others have legitimate
reasons for occasional tardiness, such as a flat tire or “He
threw up on me.” Either way, I’m hard-nosed enough not
to see them immediately if they arrive at my office more
than 10 minutes behind schedule, because to do so would
delay patients who arrived on time. Anyone who is less
than 10 minutes late is seen right away, but is reminded
of what the appointment time was.
When it’s exactly 10 minutes past the time reserved
for a patient and he hasn’t appeared at the office, a receptionist phones his home to arrange a later appointment.
If there’s no answer and the patient arrives at the office a
few minutes later, the receptionist says pleasantly, “Hey,
we were looking for you. The doctor’s had to go ahead
with his other appointments, but we’ll squeeze you in as
Workcenter Scheduling
soon as we can.” A note is then made in the patient’s chart
showing the date, how late he was, and whether he was
seen that day or given another appointment. This helps us
identify the rare chronic offender and take stronger measures if necessary.
Most people appear not to mind waiting if they know
they themselves have caused the delay. And I’d rather
incur the anger of the rare person who does mind than
risk the ill will of the many patients who would otherwise
have to wait after coming in on schedule. Although I’m
prepared to be firm with parents, this is rarely necessary.
My office in no way resembles an army camp. On the
contrary, most people are happy with the way we run it,
and tell us so frequently.
Coping with No-Shows
What about the patient who has an appointment, doesn’t
turn up at all, and can’t be reached by telephone? Those
facts, too, are noted in the chart. Usually there’s a simple
explanation, such as being out of town and f­orgetting
about the appointment. If it happens a second time,
we follow the same procedure. A third-time offender,
though, receives a letter reminding him that time was set
aside for him and he failed to keep three appointments. In
the future, he’s told, he’ll be billed for such wasted time.
That’s about as tough as we ever get with the few people
who foul up our scheduling. I’ve never dropped a patient for
doing so. In fact, I can’t recall actually billing a no-show; the
letter threatening to do so seems to cure them. And when
they come back—as nearly all of them do—they enjoy the
same respect and convenience as my other patients.
Chapter 22
621
Question s
1. What features of the appointment scheduling
system were crucial in capturing “many grateful
patients”?
2. What procedures were followed to keep the
appointment system flexible enough to accommodate the emergency cases, and yet be able to keep
up with the other patients’ appointments?
3. How were the special cases such as latecomers and
no-shows handled?
4. Prepare a schedule starting at 9 A.M. for the following patients of Dr. Schafer:
Johnny Appleseed, a splinter on his left thumb.
Mark Borino, a new patient.
Joyce Chang, a new patient.
Amar Gavhane, 102.5 degree (Fahrenheit) fever.
Sarah Goodsmith, an immunization.
Tonya Johnston, well-baby checkup.
JJ Lopez, a new patient.
Angel Ramirez, well-baby checkup.
Bobby Toolright, recheck on a sprained ankle.
Rebecca White, a new patient.
Dr. Schafer starts work promptly at 9 A.M. and
enjoys taking a 15-minute coffee break around
10:15 or 10:30 A.M.
Apply the priority rule that maximizes scheduling efficiency. Indicate whether or not you see
an exception to this priority rule that might arise.
Round up any times listed in the case study (e.g.,
if the case study stipulates 5 or 10 minutes, then
assume 10 minutes for the sake of this problem).
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. This is the currently used term for a system that
schedules, dispatches, tracks, monitors, and controls
production.
2. This is when work is assigned to workcenters based
simply on when it is needed. Resources required to
complete the work are not considered.
3. This is when detailed schedules are constructed that
­consider the setup and run times required for each order.
4. This is when work is scheduled from a point in time
and out into the future, in essence telling the earliest
the work can be completed.
5. This is when work is scheduled in reverse from a future
due date, to tell the time original work must be started.
6. If we were to coin the phrase “dual constrained”
relative to the resources being scheduled, we would
probably be referring to what two resources?
7. For a single machine scheduling problem, what
­
priority rule guarantees that the average flow time is
minimized?
8. Consider the following three jobs that need to be
run on two machines in sequence: A(3 1), B(2 2),
and C(1 3), where the run times on the first and second machine are given in parenthesis. In what order
should the jobs be run to minimize the total time to
complete all three jobs?
9. According to APICS, this is a system for utilizing
data from the shop as well as data processing files
to maintain and communicate status information on
shop orders and workcenters.
10. A resource that limits the output of a process by limiting capacity is called this.
Answers to Practice Exam 1. Manufacturing Execution System 2. Infinite scheduling 3. Finite scheduling 4. Forward scheduling 5. Backward
scheduling 6. Labor and equipment (machines) 7. Shortest operating time 8. C B A 9. Shop-floor (or production activity) control 10. Bottleneck
23
Theory of
Constraints
Learning Objectives
LO 23–1
LO 23–2
LO 23–3
LO 23–4
Explain the Theory of Constraints (TOC).
Analyze bottleneck resources and apply TOC principles to controlling a process.
Compare TOC to conventional approaches.
Evaluate bottleneck scheduling problems by applying TOC principles.
This chapter is about the ideas of management guru Eli Goldratt. He proposed the
idea that managing “constraints” is the key to maximizing the throughput and efficiency of business processes. He argued that a manager should focus on managing the resource that most limits the process from achieving its goal. This resource
is called the “bottleneck” and nothing can be achieved beyond the capability of the
bottleneck. He suggests a simple repetitive cycle for improving a process. Step 1: Find
the weakest step in the process, the step that is limiting performance the most. Step 2:
Improve that weakest step so that it is no longer limiting performance. Step 3: Repeat
steps 1 and 2 over and over again making the process better with each cycle.
To explain his ideas in an easy to understand way, Goldratt wrote a book titled The
Goal. The book tracks the life of Alex Rogo, a plant manager struggling with keeping
his plant on schedule, reducing inventory, meeting quality goals, and cutting costs.
Alex’s job is on the line and his boss has given him three months to make the plant
productive, otherwise it will be closed.
The most insightful analogy in the book is
the description of a 20-mile overnight hike
that Alex takes with his son. Alex is leading his
son’s Boy Scout troop on a hike that will take
them to a site 10 miles away where they will
spend the night. The troop will then return the
following morning after breakfast.
The analogy starts by describing the hike
out to the campsite. They are way behind
schedule and the line of scouts is spread out
over a long distance. The fastest kids are up
front, and poor Herbie, the slowest kid, lags
way behind at the end of the line. The goal is
© dolgachov/123RF
622
to get all the kids to the campsite as quickly as possible so they can get the tents
setup, have dinner, and enjoy some camp fire fun. Nothing can happen until all the
kids make it to the campsite.
Alex analyzes the situation and can see that Andy, the first kid in line is trying to set a
speed record. Herbie, who is way in the back, is the bottleneck. Herbie just cannot move
fast enough to keep up with Andy. Alex checks the speed of Andy and finds his pace
is three miles per hour and that compared to the speed of Herbie he will be two miles
ahead in less than an hour. In two hours, the stragglers will be four miles behind! The plan
had been to cover the 10 miles in five hours. Something needed to be done, and quickly.
Alex stops the leaders and tells everyone in the troop to hold hands with the person before and after him, and to not let go. He then takes Herbie, who is in the back,
and leads him to the front of the line. He keeps walking with Herbie turning the troop
around so that Herbie, the slowest, is now leading and Andy, the fastest, is now at the
end. Alex tells the troop that the goal of the hike is not to get there the fastest, but to
get there together. The troop is a team—not a bunch of individuals.
And so the troop moves on with Herbie in the lead. The line is now tight with no
gaps between the scouts. The scouts in the back of the line begin complaining that
they want to go faster. Alex tells the troop they if they want to go faster, they need to
figure out a way Herbie can go faster.
When the scouts check out Herbie they find that he is carrying a backpack much
heavier than the others. He has soda, cans of spaghetti, candy bars, and all kinds of
other stuff that the others are not carrying. No wonder he is so much slower. So the
others decide to take some of the load off Herbie by carrying some of his stuff. Now
Herbie can really move, since most of the weight in his pack is removed. The troop is
now moving at twice the speed it was before and they are still staying together.
That night Alex thought about the analogy between the troop hike and his plant.
Most of his machines were fast, but the slowest one always kept the jobs from getting
done. This causes inventory in the plant to keep increasing, and lead-time to increase
as well. He needed to tie all the processes in his plant together; there is no reason for
any of them to process any faster than that slow bottleneck process. Then he needed
to figure out how he could get more output from that bottleneck. Possibly, he could
buy another machine, or run some overtime on that machine. Only in this way could
he decrease his inventory, and increase throughput. Alex had learned a lot on his
son’s camping trip.
ELI G OLDRATT’S T HEORY OF CONSTRAINTS
The story of Herbie is an analogy to the problems facing plant manager Alex Rogo and comes
from a best-selling novel, The Goal, by Dr. Eli Goldratt. Around 1980, Goldratt contended
that manufacturers were not doing a good job in scheduling and controlling their resources and
inventories. To solve this problem, Goldratt and his associates, at a company named Creative
Output, developed software that scheduled jobs through manufacturing processes, taking into
account limited facilities, machines, personnel, tools, materials, and any other constraints that
would affect a firm’s ability to adhere to a schedule.
LO 23–1
Explain the Theory of
Constraints (TOC).
623
624
Section 4
Synchronous
manufacturing
A production process
coordinated to work in
harmony to achieve the
goals of the firm.
Supply and Demand Planning and Control
This was called optimized production technology (OPT). The schedules were feasible and
accurate and could be run on a computer in a fraction of the time needed by an MRP system. This
was because the scheduling logic was based on the separation of bottleneck and nonbottleneck
operations. To explain the principles behind the OPT scheduling logic, Goldratt described nine
production scheduling rules (see Exhibit 23.1). After approximately 100 large firms had installed
this software, Goldratt went on to promote the logic of the approach rather than the software.
In broadening his scope, Goldratt developed his “Theory of Constraints” (TOC), which has
become popular as a problem-solving approach that can be applied to many business areas.
Exhibit 23.2 lists the “Five Focusing Steps of TOC.” His Goldratt Institute (www.goldratt.com)
teaches courses in improving production, distribution, and project management. The common
thread through all of these courses is Goldratt’s TOC concepts.
Before we go into detail on the theory of constraints, it is useful to compare it with two
other popular approaches to continuous improvement: Six Sigma and lean manufacturing.
Both Six Sigma and lean approaches focus on cost reduction through the elimination of waste
and the reduction of variability at every step in a process or in view of every component of a
system. In contrast, the TOC five-step approach is more focused in its application. It concentrates its improvement efforts only on the operation that is constraining a critical process or
on the weakest component that is limiting the performance of the system as a whole. If these
elements are effectively managed, then it follows that better overall performance of the system
relative to its goal is more likely to be achieved.
In this chapter, we focus on Goldratt’s approach to manufacturing. To correctly treat the
topic, we decided to approach it in the same way that Goldratt did: that is, by first defining
some basic issues about firms—purposes, goals, and performance measures—and then dealing with scheduling, providing buffer inventories, focusing on the influences of quality, and
looking at interactions with marketing and accounting.
Underlying Goldratt’s work is the notion of synchronous manufacturing, which refers
to the entire production process working in harmony to achieve the profit goal of the firm.
exhibit 23.1
Goldratt’s Rules of Production Scheduling
1. Do not balance capacity—balance the flow.
2. The level of utilization of a nonbottleneck resource is determined not by its own potential but by
some other constraint in the system.
3. Utilization and activation of a resource are not the same.
4. An hour lost at a bottleneck is an hour lost for the entire system.
5. An hour saved at a nonbottleneck is a mirage.
6. Bottlenecks govern both throughput and inventory in the system.
7. The transfer batch may not, and many times should not, be equal to the process batch.
8. A process batch should be variable both along its route and in time.
9. Priorities can be set only by examining the system’s constraints. Lead time is a derivative of the schedule.
exhibit 23.2
Goldratt’s Theory of Constraints (TOC)
1. Identify the system constraints. (No improvement is possible unless the constraint or weakest link is
found.)
2. Decide how to exploit the system constraints. (Make the constraints as effective as possible.)
3. Subordinate everything else to that decision. (Align every other part of the system to support the
constraints even if this reduces the efficiency of nonconstraint resources.)
4. Elevate the system constraints. (If output is still inadequate, acquire more of this resource so it no
longer is a constraint.)
5. If, in the previous steps, the constraints have been broken, go back to Step 1, but do not let inertia
become the system constraint. (After this constraint problem is solved, go back to the beginning and
start over. This is a continuous process of improvement: identifying constraints, breaking them, and
then identifying the new ones that result.)
Theory of Constraints
Chapter 23
625
When manufacturing is truly synchronized, its emphasis is on total system performance, not
on localized measures such as labor or machine utilization.
T h e G oa l of the Fir m
Goldratt has a very straightforward idea about the goal of any firm:
THE GOAL OF A FIRM IS TO MAKE MONEY.
Goldratt argues that although an organization may have many purposes—providing jobs, consuming raw materials, increasing sales, increasing share of the market, developing technology,
or producing high-quality products—these do not guarantee long-term survival of the firm.
They are means to achieve the goal, not the goal itself. If the firm makes money—and only
then—it will prosper. When a firm has money, it can place more emphasis on other objectives.
Pe r for m a nce M e a s ur e me n ts
To adequately measure a firm’s performance, two sets of measurements must be used: one
from the financial point of view and the other from the operations point of view.
F i n a n c i a l M e a s u r e m e n t s We have three measures of the firm’s ability to make
money:
1.
2.
3.
Net profit—an absolute measurement in dollars.
Return on investment—a relative measure based on investment.
Cash flow—a survival measurement.
All three measurements must be used together. For example, a net profit of $10 million is
important as one measurement, but it has no real meaning until we know how much investment was needed to generate that $10 million. If the investment was $100 million, this is a
10 percent return on investment. Cash flow is important because cash is necessary to pay bills
for day-to-day operations; without cash, a firm can go bankrupt even though it is very sound
in normal accounting terms. A firm can have a high profit and a high return on investment
but still be short on cash if, for example, profit is invested in new equipment or tied up in
inventory.
O p e r a t i o n a l M e a s u r e m e n t s Financial measurements work well at the higher
level, but they cannot be used at the operational level. We need another set of measurements
that will give us guidance:
1.
2.
3.
Throughput—the rate at which money is generated by the system through sales.
Inventory—all the money that the system has invested in purchasing things it
intends to sell.
Operating expenses—all the money that the system spends to turn inventory into
throughput.
Throughput is specifically defined as goods sold. An inventory of finished goods is not
throughput, but inventory. Actual sales must occur. It is specifically defined this way to prevent the system from continuing to produce under the illusion that the goods might be sold.
Such action simply increases costs, builds inventory, and consumes cash. Inventory that is
carried (whether work-in-process or finished goods) is valued only at the cost of the materials it contains. Labor cost and machine hours are ignored. (In traditional accounting terms,
money spent is called value added.)
Although this is often an arguable point, using only the raw material cost is a conservative
view. When the value-added method (which includes all costs of production) is used, inventory is inflated and presents some serious income and balance sheet problems. Consider, for
example, work-in-process or finished-goods inventory that has become obsolete, or for which
Throughput
The rate at which money is
generated by the system
through sales (Goldratt’s
definition).
Inventory (Goldratt’s
definition)
All the money that the
system has invested
in purchasing things it
intends to sell.
Operating expenses
All the money that the
system spends to turn
inventory into throughput
(Goldratt’s definition).
626
Section 4
Supply and Demand Planning and Control
a contract was canceled. A management decision to declare large amounts of inventory as
scrap is difficult because it is often carried on the books as an asset even though it may really
have no value. Using just raw materials cost also avoids the problem of determining which
costs are direct and which are indirect.
Operating expenses include production costs (such as direct labor, indirect labor, inventory
carrying costs, equipment depreciation, and materials and supplies used in production) and
administrative costs. The key difference here is that there is no need to separate direct and
indirect labor.
As shown in Exhibit 23.3, the objective of a firm is to treat all three measurements simultaneously and continually; this achieves the goal of making money.
From an operations standpoint, the goal of the firm is to
INCREASE THROUGHPUT WHILE SIMULTANEOUSLY REDUCING
INVENTORY AND REDUCING OPERATING EXPENSE.
Productivity
A measure of how well
resources are used.
According to Goldratt’s
definition (see Chapter 23),
all the actions that bring
a company closer to its
goals.
P r o d u c t i v i t y Typically, productivity is measured in terms of output per labor hour.
However, this measurement does not ensure that the firm will make money (for example,
when extra output is not sold but accumulates as inventory). To test whether productivity has
increased, we should ask these questions: Has the action taken increased throughput? Has it
decreased inventory? Has it decreased operational expense? This leads us to a new definition:
PRODUCTIVITY IS ALL THE ACTIONS THAT BRING A COMPANY
CLOSER TO ITS GOALS.
U nba la nce d Cap acit y
Historically (and still typically in most firms), manufacturers have tried to balance capacity
across a sequence of processes in an attempt to match capacity with market demand. However,
this is the wrong thing to do—unbalanced capacity is better. The vignette at the beginning
of this chapter is an example of unbalanced capacity. Some Boy Scouts were fast walkers,
whereas Herbie was very slow. The challenge is to use this difference advantageously.
Consider a simple process line with several stations, for example. Once the output rate of
the line has been established, production people try to make the capacities of all stations the
same. This is done by adjusting machines or equipment used, workloads, skill and type of
labor assigned, tools used, overtime budgeted, and so on.
In synchronous manufacturing thinking, however, making all capacities the same is viewed
as a bad decision. Such a balance would be possible only if the output times of all stations
were constant or had a very narrow distribution. A normal variation in output times causes
downstream stations to have idle time when upstream stations take longer to process. Conversely, when upstream stations process in a shorter time, inventory builds up between the
stations. The effect of the statistical variation is cumulative. The only way that this variation can be smoothed is by increasing work-in-process to absorb the variation (a bad choice
because we should be trying to reduce work-in-process) or increasing capacities downstream
exhibit 23.3
Operational Goal
Throughput
T
I
OE
Inventory
Operating expense
The operational goal of a firm is to increase throughput while reducing inventory and operating expense.
Theory of Constraints
627
Chapter 23
to be able to make up for the longer upstream times. The rule here is that capacities within
the process sequence should not be balanced to the same levels. Rather, attempts should be
made to balance the flow of product through the system. When flow is balanced, capacities
are unbalanced. This idea is further explained in the next section.
D e p e n d e n t E v e n t s a n d S t a t i s t i c a l F l u c t u a t i o n s The term dependent
events refers to a process sequence. If a process flows from A to B to C to D, and each process
must be completed before passing on to the next step, then B, C, and D are dependent events.
The ability to do the next process is dependent on the preceding one.
Statistical fluctuation refers to the normal variation about a mean or average. When statistical fluctuations occur in a dependent sequence without any inventory between workstations,
there is no opportunity to achieve the average output. When one process takes longer than the
average, the next process cannot make up the time. We follow through an example of this to
show what could happen.
Suppose we wanted to process five items that could come from the two distributions in
Exhibit 23.4. The processing sequence is from A to B, with no space for inventory in between.
Process A has a mean of 10 hours and a standard deviation of 2 hours. This means we would
expect 95.5 percent of the processing time to be between 6 hours and 14 hours (plus or minus
2 sigma). Process B has a constant processing time of 10 hours.
We see that the last item was completed in 66 hours, for an average of 13.2 hours per item,
although the expected time of completion was 60, for an average of 12 hours per item (taking
into account the waiting time for the first unit by Process B).
Suppose we reverse the processes—B feeds A. To illustrate the possible delays, we also
reverse A’s performance times. (See Exhibit 23.5.) Again, the completion time of the last item
is greater than the average (13.2 hours rather than 12 hours). Process A and Process B have
the same average performance time of 10 hours, and yet performance is late. In neither case
could we achieve the expected average output rate. Why? Because the time lost when the second process is idle cannot be made up.
This example is intended to challenge the theory that capacities should be balanced to an
average time. Rather than capacities being balanced, the flow of product through the system
should be balanced.
ex hibit 23.4
Processing and Completion Times, Process A to Process B
Process A
Process B
No variability in
processing time
6
8
10
12
14
6
8
10
12
Item
Number
Start
Time
Processing
Time
Finish
Time
Item
Number
Start
Time
Processing
Time
Finish
Time
1
0 hrs
14 hrs
14 hrs
1
14 hrs
10 hrs
24 hrs
2
14
12
26
2
26
10
36
3
26
10
36
3
36
10
46
4
36
8
44
4
46
10
56
5
44
6
50
5
56
10
66
Average = 10 hours
14
Average = 10 hours
Here the flow is from Process A (on the left) to Process B (on the right). Process A has a mean of 10 hours and a standard deviation
of 2 hours; Process B has a constant 10-hour processing time.
628
Supply and Demand Planning and Control
Section 4
Processing and Completion Times, Process A to Process B
exhibit 23.5
Process B
Process A
No variability
in processing time
8
6
10
12
14
6
8
10
12
Item
Number
Start
Time
Processing
Time
Finish
Time
Item
Number
Start
Time
Processing
Time
Finish
Time
1
0 hrs
10 hrs
10 hrs
1
10 hrs
6 hrs
16 hrs
2
10
10
20
2
20
8
28
3
20
10
30
3
30
10
40
4
30
10
40
4
40
12
52
5
40
10
50
5
52
14
66
Average = 10 hours
14
Average = 10 hours
This is similar to Exhibit 23.4. However, the processing sequence has been reversed, as well as the order of the Process A times.
BOTTLENECKS, CAPACITY-CONSTRAINED RESOURCES,
AND SY NCHRONOU S MANUFACTURING
LO 23–2
Analyze bottleneck
resources and apply TOC
principles to controlling a
process.
Bottleneck
A resource that limits the
capacity or maximum
output of the process.
Nonbottleneck
Any resource whose
capacity is greater than
the demand placed on it
(Goldratt’s definition).
Capacity-constrained
resource (CCR)
A resource whose
utilization is close to
capacity and could be a
bottleneck if not scheduled
carefully (Goldratt’s
definition).
A bottleneck is defined as any resource whose capacity is less than the demand placed upon
it. A bottleneck is a constraint within the system that limits throughput. It is that point in the
manufacturing process where flow thins to a narrow stream. A bottleneck may be a machine,
scarce or highly skilled labor, or a specialized tool. Observations in industry have shown that
most plants have very few bottleneck operations.
If there is no bottleneck, then excess capacity exists and the system should be changed to
create a bottleneck (such as more setups or reduced capacity), which we will discuss later.
Capacity is defined as the available time for production. This excludes maintenance and
other downtime. A nonbottleneck is any resource whose capacity is greater than the demand
placed on it. A nonbottleneck, therefore, should not be working constantly because it can produce more than is needed. A nonbottleneck contains idle time.
A capacity-constrained resource (CCR) is one whose utilization is close to capacity and
could be a bottleneck if it is not scheduled carefully. For example, a CCR may be receiving
work in a job-shop environment from several sources. If these sources schedule their flow in
a way that causes occasional idle time for the CCR in excess of its unused capacity time, the
CCR becomes a bottleneck when the surge of work arrives at a later time. This can happen if
batch sizes are changed or if one of the upstream operations is not working for some reason
and does not feed enough work to the CCR.
B a s ic M a n u f a ct u rin g Bu ild in g Blo cks
All manufacturing processes and flows can be simplified to four basic configurations, as
shown in Exhibit 23.6. In configuration A of Exhibit 23.6, product that flows through Process
X feeds into Process Y. In configuration B, Y is feeding X. In C, Process X and Process Y
are creating subassemblies, which are then combined, say, to feed the market demand. In D,
Process X and Process Y are independent of each other and are supplying their own markets.
The last column in the exhibit shows possible sequences of nonbottleneck resources, which
can be grouped and displayed as Y to simplify the representation.
Theory of Constraints
ex hibit 23.6
629
Chapter 23
The Basic Building Blocks of Manufacturing Derived by Grouping Process Flows
DESCRIPTION
BASIC BUILDING BLOCKS SIMPLIFIED
BY GROUPING NONBOTTLENECKS
ORIGINAL REPRESENTATION
Y
A. Bottleneck feeding
nonbottleneck
X
B. Nonbottleneck feeding
bottleneck
Y
C. Output of bottleneck and
nonbottleneck assembled
into a product
D. Bottleneck and nonbottleneck
have independent markets
for their output
X is a bottleneck.
Y is a nonbottleneck (has excess capacity).
Y
A
X
Market
B
C
D
Market
C
D
X
Market
Y
X
Y
X
Y
X
Final
Assembly
Market
B
A
Market
X
Market
Y
A
B
C
A
D
Final
Assembly
Y
B
C
Market
The value in using these basic building blocks is that a production process can be greatly
simplified for analysis and control. Rather than track and schedule all of the steps in a production sequence through nonbottleneck operations, for example, attention can be placed at the
beginning and end points of the building block groupings.
M e t h od s for Synchr ono u s C o n tro l
Exhibit 23.7 shows how bottleneck and nonbottleneck resources should be managed.
Resource X and Resource Y are workcenters that can produce a variety of products. Each
of these workcenters has 200 hours available per month. For simplicity, assume that we are
dealing with only one product and we will alter the conditions and makeup for four different situations. Each unit of X takes one hour of production time, and the market demand is
200 units per month. Each unit of Y takes 45 minutes of production time, and the market
demand is also 200 units per month.
Exhibit 23.7A shows a bottleneck feeding a nonbottleneck. Product flows from Workcenter X to Workcenter Y. X is the bottleneck because it has a capacity of 200 units (200 hours/
1 hour per unit) and Y has a capacity of 267 units (200 hours/45 minutes per unit). Because
Y has to wait for X, and Y has a higher capacity than X, no extra product accumulates in the
system. It all flows through to the market.
Exhibit 23.7B is the reverse of A, with Y feeding X. This is a nonbottleneck feeding a
bottleneck. Because Y has a capacity of 267 units and X has a capacity of only 200 units,
we should produce only 200 units of Y (75 percent of capacity) or else work-in-process will
accumulate in front of X.
Exhibit 23.7C shows that the products produced by X and Y are assembled and then sold to
the market. Because one unit from X and one unit from Y form an assembly, X is the bottleneck with 200 units of capacity and, therefore, Y should not work more than 75 percent or else
extra parts will accumulate.
In Exhibit 23.7D, equal quantities of product from X and Y are demanded by the market. In this case, we can call these products “finished goods” because they face independent
demands. Here, Y has access to material independent of X and, with a higher capacity than
needed to satisfy the market (in essence, the market is the bottleneck), it can produce more
product than the market will take. However, this would create an inventory of unneeded finished goods.
X
D
Market
Market
Market
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Supply and Demand Planning and Control
Section 4
exhibit 23.7
Product Flow through Bottlenecks and Nonbottlenecks
A.
B.
X
Y
200 units
of product
(200 hours)
200 units
of product
(150 hours)
WIP
Y
Market
X
Market
Y can be used only 75% of the time
or work-in-process will build up.
200 = 100%
X used ___
200
___
Y used 150 = 75%
200
Market
C.
D.
Market
Market
FG
Assembly
X
Spare parts
X
Y
Y
Y can be used only 75% of the time
or spare parts will accumulate.
Y can be used only 75% of the time
or finished goods inventory will build up.
X is a bottleneck; Y is a nonbottleneck. Both X and Y have 200 hours available.
The four situations just discussed demonstrate bottleneck and nonbottleneck resources and
their relationships to production and market demand. They show that the industry practice
of using resource utilization as a measure of performance can encourage the overuse of nonbottlenecks and result in excess inventories.
T i m e C o m p o n e n t s The following kinds of time make up production cycle time:
1.
2.
3.
4.
5.
Setup time—the time that a part spends waiting for a resource to be set up to work on
this same part.
Processing time—the time that the part is being processed.
Queue time—the time that a part waits for a resource while the resource is busy with
something else.
Wait time—the time that a part waits not for a resource but for another part so that
they can be assembled together.
Idle time—the unused time; that is, the cycle time minus the sum of the setup time,
processing time, queue time, and wait time.
For a part waiting to go through a bottleneck, queue time is usually the greatest. As we
discuss later in this chapter, this is because the bottleneck has a fairly large amount of work
to do in front of it (to make sure it is always working). For a nonbottleneck, wait time is usually the greatest. The part is just sitting there waiting for the arrival of other parts so that an
assembly can take place.
Schedulers are tempted to save setup times. Suppose that the batch sizes are doubled to
save half the setup times. Then, with a double batch size, all of the other times (processing
time, queue time, and wait time) increase twofold. Because these times are doubled while
saving only half of the setup time, the net result is that the work-in-process is approximately
doubled, as is the investment in inventory.
F i n d i n g t h e B o t t l e n e c k There are two ways to find the bottleneck (or bottlenecks)
in a system. One is to run a capacity resource profile; the other is to use our knowledge of the
particular plant, look at the system in operation, and talk with supervisors and workers.
Theory of Constraints
Chapter 23
A capacity resource profile is obtained by looking at the loads placed on each resource
by the products that are scheduled through them. In running a capacity profile, we assume
that the data are reasonably accurate, although not necessarily perfect. As an example, consider that products have been routed through Resources M1 through M5. Suppose that our
first computation of the resource loads on each resource caused by these products shows the
following:
M1 130 percent of capacity
M2 120 percent of capacity
M3​
​
​ 105 percent of capacity​​ ​
M4 95 percent of capacity
M5 85 percent of capacity
For this first analysis, we can disregard any resources at lower percentages because they
are nonbottlenecks and should not be a problem. With this list in hand, we should physically
go to the facility and check all five operations. Note that M1, M2, and M3 are overloaded; that
is, they are scheduled above their capacities. We would expect to see large quantities of inventory in front of M1. If this is not the case, errors must exist somewhere—perhaps in the bill
of materials or in the routing sheets. Let’s say that our observations and discussions with shop
personnel showed that there were errors in M1, M2, M3, and M4. We tracked them down,
made the appropriate corrections, and ran the capacity profile again:
M1 115 percent of capacity
M2 110 percent of capacity
M3​
​
​ 105 percent of capacity​​ ​
M4 90 percent of capacity
M5 85 percent of capacity
M1, M2, and M3 are still showing a lack of sufficient capacity, but M2 is the most serious.
If we now have confidence in our numbers, we use M2 as our bottleneck. If the data contain
too many errors for a reliable data analysis, it may not be worth spending time (it could take
months) making all the corrections.
S a v i n g T i m e Recall that a bottleneck is a resource whose capacity is less than the
demand placed on it. Because we focus on bottlenecks as restricting throughput (defined as
sales), a bottleneck’s capacity is less than the market demand. There are a number of ways we
can save time on a bottleneck (better tooling, higher-quality labor, larger batch sizes, reduction
in setup times, and so forth), but how valuable is the extra time? Very, very valuable!
AN HOUR SAVED AT THE BOTTLENECK ADDS AN EXTRA HOUR
TO THE ENTIRE PRODUCTION SYSTEM.
How about time saved on a nonbottleneck resource?
AN HOUR SAVED AT A NONBOTTLENECK IS A MIRAGE AND
ONLY ADDS AN HOUR TO ITS IDLE TIME.
Because a nonbottleneck has more capacity than the system needs for its current throughput, it already contains idle time. Implementing any measures to save more time does not
increase throughput but only serves to increase its idle time.
Avoid Changing a Nonbottleneck into a Bottleneck When nonbottleneck resources
are scheduled with larger batch sizes, this action could create a bottleneck that we certainly
would want to avoid. Consider the case in Exhibit 23.8, where Y1, Y2, and Y3 are nonbottleneck
resources. Y1 currently produces Part A, which is routed to Y3, and Part B, which is routed to
Y2. To produce Part A, Y1 has a 200-minute setup time and a processing time of 1 minute per
part. Part A is currently produced in batches of 500 units. To produce Part B, Y1 has a setup
631
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Supply and Demand Planning and Control
exhibit 23.8
Utilization 70%
Nonbottleneck Resources
Y3
Y2
Part B
Utilization 80%
Part A
Y1
Part A: Batch size = 500 pieces
Setup time = 200 minutes
Processing time = 1 minute/part
Part B: Batch size = 200 pieces
Setup time = 150 minutes
Processing time = 2 minutes/part
Resource Y1 produces Part A for Resource Y3 and Part B for Resource Y2.
time of 150 minutes and 2 minutes’ processing time per part. Part B is currently produced
in batches of 200 units. With this sequence, Y2 is utilized 70 percent of the time and Y3 is
utilized 80 percent of the time.
Because setup time is 200 minutes for Y1 on Part A, both worker and supervisor mistakenly believe that more production can be gained if fewer setups are made. Let’s assume that
the batch size is increased to 1,500 units and see what happens. The illusion is that we have
saved 400 minutes of setup. (Instead of three setups taking 600 minutes to produce three
batches of 500 units each, there is just one setup with a 1,500-unit batch.)
The problem is that the 400 minutes saved served no purpose, but this delay did interfere with
the production of Part B because Y1 produces Part B for Y2. The sequence before any changes were
made was Part A (700 minutes), Part B (550 minutes), Part A (700 minutes), Part B (550 minutes), and so on. Now, however, when the Part A batch is increased to 1,500 units (1,700 minutes),
Y2 and Y3 could well be starved for work and have to wait more time than they have available
(30 percent idle time for Y2 and 20 percent for Y3). The new sequence would be Part A (1,700
minutes), Part B (1,350 minutes), and so on. Such an extended wait for Y2 and Y3 could be disruptive. Y2 and Y3 could become temporary bottlenecks and lose throughput for the system.
D r u m , B u f f e r , R o p e Every production system needs some control point or points
to control the flow of product through the system. If the system contains a bottleneck, the
bottleneck is the best place for control. This control point is called the drum because it strikes
the beat that the rest of the system (or those parts that it influences) uses to function. Recall
that a bottleneck is defined as a resource that does not have the capacity to meet demand.
Therefore, a bottleneck is working all the time, and one reason for using it as a control point
is to make sure that the operations upstream do not overproduce and build up excess work-inprocess inventory that the bottleneck cannot handle.
If there is no bottleneck, the next-best place to set the drum would be a capacity-­constrained
resource (CCR). A capacity-constrained resource, remember, is one that is operating near
capacity but, on average, has adequate capability as long as it is not incorrectly scheduled (for
example, with too many setups, causing it to run short of capacity, or producing too large a lot
size, thereby starving downstream operations).
If neither a bottleneck nor a CCR is present, the control point can be designated anywhere.
The best position would generally be at some divergent point where the output of the resource
is used in several downstream operations.
Dealing with the bottleneck is most critical, and our discussion focuses on ensuring that
the bottleneck always has work to do. Exhibit 23.9 shows a simple linear flow A through
G. Suppose that Resource D, which is a machine center, is a bottleneck. This means the capacities are greater both upstream and downstream from it. If this sequence is not controlled, we
Theory of Constraints
ex hibit 23.9
Chapter 23
Linear Flow of Product with a Bottleneck
Bottleneck (drum)
A
C
B
D
E
F
G
Market
Inventory
(buffer)
Communication
(rope)
Product flows from Workcenters A through G. Workcenter D is a bottleneck.
would expect to see a large amount of inventory in front of Workcenter D and very little anywhere else. There would be little finished goods inventory because (by the definition of the
term bottleneck) all the product produced would be taken by the market.
There are two things we must do with this bottleneck:
1.
2.
Keep a buffer inventory in front of it to make sure it always has something to work
on. Because it is a bottleneck, its output determines the throughput of the system.
Communicate back upstream to A what D has produced so that A provides only that
amount. This keeps inventory from building up. This communication is called the
rope. It can be formal (such as a schedule) or informal (such as daily discussion).
The buffer inventory in front of a bottleneck operation is a time buffer. We want to make
sure that Workcenter D always has work to do, and it does not matter which of the scheduled
products are worked on. We might, for example, provide 96 hours of inventory in the buffer
as shown in the sequence A through P in Exhibit 23.10. Jobs A through about half of E are
scheduled during the 24 hours of Day 1; Jobs E through a portion of Job I are scheduled during the second 24-hour day; Jobs I through part of L are scheduled during the third 24-hour
day; and Jobs L through P are scheduled during the fourth 24-hour day, for a total of 96 hours.
This means that through normal variation, or if something happens upstream and the output
has been temporarily stalled, D can work for another 96 hours, protecting the throughput.
(The 96 hours of work, incidentally, include setups and processing times contained in the job
sheets, which usually are based on engineering standard times.)
We might ask, How large should the time buffer be? The answer: As large as it needs to be
to ensure that the bottleneck continues to work. By examining the variation of each operation,
we can make a guess. Theoretically, the size of the buffer can be computed statistically by
ex hibit 23.10
Capacity Profile of Workcenter D (showing assigned jobs A through P
over a period of four 24-hour days)
24
20
Hours
Workcenter D
E
I
16
D
12
C
G
8
B
F
A
E
4
L
P
K
O
H
1
2
J
N
M
I
L
Days
3
4
633
634
Section 4
Supply and Demand Planning and Control
examining past performance data, or the sequence can be simulated. In any event, precision is
not critical. We could start with an estimate of the time buffer as one-fourth of the total lead
time of the system. Say, the sequence A to G in our example (Exhibit 23.9) took a total of
16 days. We could start with a buffer of four days in front of D. If, during the next few days or
weeks, the buffer runs out, we need to increase the buffer size. We do this by releasing extra
material to the first operation, A. On the other hand, if we find that our buffer never drops
below three days, we might want to hold back releases to A and reduce the time buffer to three
days. Experience is the best determination of the final buffer size.
If the drum is not a bottleneck but a CCR (and thus it can have a small amount of idle
time), we might want to create two buffer inventories: one in front of the CCR and the second
at the end as finished goods. (See Exhibit 23.11.) The finished-goods inventory protects the
market, and the time buffer in front of the CCR protects throughput. For this CCR case, the
market cannot take all that we can produce, so we want to ensure that finished goods are available when the market does decide to purchase.
We need two ropes in this case: (1) a rope communicating from finished-goods inventory
back to the drum to increase or decrease output and (2) a rope from the drum back to the
material release point, specifying how much material is needed.
Exhibit 23.12 is a more detailed network flow showing one bottleneck. Inventory is
­provided not only in front of that bottleneck but also after the nonbottleneck sequence of processes that feed the subassembly. This ensures that the flow of product is not slowed down by
having to wait after it leaves the bottleneck.
I m p o r t a n c e o f Q u a l i t y An MRP system allows for rejects by building a larger
batch than actually needed. A JIT system cannot tolerate poor quality because JIT success is
based on a balanced capacity. A defective part or component can cause a JIT system to shut
down, thereby losing throughput of the total system. Synchronous manufacturing, however,
has excess capacity throughout the system, except for the bottleneck. If a bad part is produced
upstream of the bottleneck, the result is that there is a loss of material only. Because of the
excess capacity, there is still time to do another operation to replace the one just scrapped.
For the bottleneck, however, extra time does not exist, so there should be a quality control
inspection just prior to the bottleneck to ensure that the bottleneck works only on good
product. Also, there needs to be assurance downstream from the bottleneck that the passing
product is not scrapped—that would mean lost throughput.
B a t c h S i z e s In an assembly line, what is the batch size? Some would say “one” because
one unit is moved at a time; others would say “infinity” because the line continues to produce
the same item. Both answers are correct, but they differ in their point of view. The first answer,
“one,” in an assembly line focuses on the part transferred one unit at a time. The second focuses
on the process. From the point of view of the resource, the process batch is infinity because it is
continuing to run the same units. Thus, in an assembly line, we have a process batch of infinity
(or all the units until we change to another process setup) and a transfer batch of one unit.
exhibit 23.11
Linear Flow of Product with a Capacity-Constrained Resource
Capacityconstrained
resource
A
B
C
D
E
F
G
Market
FG
Buffer
Rope
H
Rope
Product flows through Workcenters A through H. Workcenter E is capacity constrained.
Buffer of
finished
goods
Theory of Constraints
ex hibit 23.12
Chapter 23
Network Flow with One Bottleneck
Customer
orders
and/or
forecasts
Assembly
Buffer inventory
Subassembly
Subassembly
Buffer inventory
Machine Center
A
(bottleneck)
Parts and
processing
sequences
Time buffer
inventory
Raw materials
Product flows from raw materials through processing to the market. Inventory buffers protect throughput.
Setup costs and carrying costs were treated in depth in Chapter 20, “Inventory Management.” In the present context, setup costs relate to the process batch and carrying costs relate
to the transfer batch.
A process batch is of a size large enough or small enough to be processed in a particular
length of time. From the point of view of a resource, two times are involved: setup time and
processing run time (ignoring downtime for maintenance or repair). Larger process batch
sizes require fewer setups and therefore can generate more processing time and more output. For bottleneck resources, larger batch sizes are desirable. For nonbottleneck resources,
smaller process batch sizes are desirable (by using up the existing idle time), thereby reducing
work-in-process inventory.
Transfer batches refer to the movement of part of the process batch. Rather than wait for
the entire batch to be finished, work that has been completed by that operation can be moved
to the next downstream workstation so it can begin working on that batch. A transfer batch can
be equal to a process batch, but it should not be larger under a properly designed system. This
could occur only if a completed process batch were held until sometime later when a second
batch was processed. If this later time was acceptable in the beginning, then both jobs should
be combined and processed together at the later time.
The advantage of using transfer batches that are smaller than the process batch quantity is that the total production time is shorter so the amount of work-in-process is smaller.
Exhibit 23.13 shows a situation where the total production lead time was reduced from 2,100
to 1,310 minutes by (1) using a transfer batch size of 100 rather than 1,000 and (2) reducing
the process batch sizes of Operation 2.
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Section 4
Effect of Changing the Process Batch Sizes on Production Lead Time for a Job Order of
1,000 Units
exhibit 23.13
Processing time
Operation 1
Operation 2
Operation 3
1.0 minute/unit
0.1 minute/unit
1.0 minute/unit
Process batch = 1,000 units
Transfer batch = 1,000 units
Process batches = Various sizes
Transfer batches = 100 units
Operation
Process
batch
Transfer
batch
1
1,000
1,000
2
1,000
1,000
3
1,000
1,000
Operation
Process
batch
Transfer
batch
1
1,000
100
2
300, 300,
200, 200
100
3
1,000
100
1,000 minutes
1,000
minutes
100
minutes
1,000
minutes
300
300 200 200
1,000 minutes
Total lead time:
2,100 minutes
Total lead time:
1,310 minutes
H o w t o D e t e r m i n e P r o c e s s B a t c h a n d T r a n s f e r B a t c h S i z e s Logic
would suggest that the master production schedule (however it was developed) be analyzed as
to its effect on various workcenters. In an MRP system, this means that the master production
schedule should be run through the MRP and the CRP (capacity requirements planning
program) to generate a detailed load on each workcenter. From this report, probable CCRs
and bottlenecks can be identified. There should be only one (or a few), and they should be
reviewed by managers so that they understand which resources are actually controlling their
plant. These resources set the drumbeat.
Rather than try to adjust the master production schedule to change resource loads, it is
more practical to control the flow at each bottleneck or CCR to bring the capacities in line.
The process batch sizes and transfer batch sizes are changed after comparing past performances in meeting due dates.
Smaller transfer batches give lower work-in-process inventory and faster product flow (and
consequently shorter lead time). More material handling is required, however. Larger transfer
batches give longer lead times and higher inventories, but there is less material handling.
Therefore, the transfer batch size is determined by a trade-off of production lead times, inventory reduction benefits, and costs of material movement.
When trying to control the flow at CCRs and bottlenecks, there are four possible situations:
1.
2.
3.
4.
A bottleneck (no idle time) with no setup time required when changing from one
product to another.
A bottleneck with setup time required to change from one product to another.
A capacity-constrained resource with a small amount of idle time, with no setup time
required to change from one product to another.
A CCR with setup time required when changing from one product to another.
In the first case (a bottleneck with no setup time to change products), jobs should be
processed in the order of the schedule so that delivery is on time. Without setups, only
the sequence is important. In the second case, when setups are required, larger batch sizes
Theory of Constraints
Chapter 23
combine separate similar jobs in the sequence. This means reaching ahead into future time
periods. Some jobs will therefore be done early. Because this is a bottleneck resource, larger
batches save setups and thereby increase throughput. (The setup time saved is used for processing.) The larger process batches may cause the early-scheduled jobs to be late. Therefore,
frequent small transfer batches are necessary to try to shorten the lead time.
Situations 3 and 4 include a CCR without a setup and a CCR with setup time requirements,
respectively. Handling the CCR would be similar to handling a nonbottleneck, though more
carefully. That is, a CCR has some idle time. It would be appropriate here to cut the size
of some of the process batches so that there can be more frequent changes of product. This
would decrease lead time, and jobs would be more likely to be done on time. In a make-tostock situation, cutting process batch sizes has a much more profound effect than increasing
the number of transfer batches. This is because the resulting product mix is much greater,
leading to reduced WIP and production lead time.
H o w t o T r e a t I n v e n t o r y The traditional view of inventory is that its only negative
impact on a firm’s performance is its carrying cost. We now realize inventory’s negative
impact also comes from lengthening lead times and creating problems with engineering
changes. (When an engineering change on a product comes through, which commonly occurs,
product still within the production system often must be modified to include the changes.
Therefore, less work-in-process reduces the amount of product rework necessary.)
From a constraint management perspective, inventory is a loan given to the manufacturing
unit. The value of the loan is based only on the purchased items that are part of the inventory.
As we stated earlier, inventory is treated in this chapter as material cost only, without any
accounting-type value added from production. If inventory is carried as a loan to manufacturing, we need a way to measure how long the loan is carried. One measurement is dollar days.
D o l l a r D a y s A useful performance measurement is the concept of dollar days, a
measurement of the value of inventory and the time it stays within an area. To use this measure,
we could simply multiply the total value of inventory by the number of days inventory spends
within a department.
Suppose Department X carries an average inventory of $40,000, and, on average, the
inventory stays within the department five days. In dollar days, Department X is charged with
$40,000 times five days, or $200,000 dollar days of inventory. At this point, we cannot say
the $200,000 is high or low, but it does show where the inventory is located. Management can
then see where it should focus attention and determine acceptable levels. Techniques can be
instituted to try to reduce the number of dollar days while being careful that such a measure
does not become a local objective (that is, minimizing dollar days) and hurt the global objectives (such as increasing ROI, cash flow, and net profit).
Dollar days could be beneficial in a variety of ways. Consider the current practice of using
efficiencies or equipment utilization as a performance measurement. To get high utilization,
large amounts of inventory are held to keep everything working. However, high inventories
would result in a high number of dollar days, which would discourage high levels of work-inprocess. Dollar day measurements also could be used in other areas:
∙
∙
∙
∙
Marketing—to discourage holding large amounts of finished-goods inventory. The net
result would be to encourage the sales of finished products.
Purchasing—to discourage placing large purchase orders that on the surface appear to
take advantage of quantity discounts. This would encourage just-in-time purchasing.
Manufacturing—to discourage large work-in-process and producing earlier than
needed. This would promote rapid flow of material within the plant.
Project management—to quantify a project’s limited resource investments as a function
of time. This promotes the proper allocation of resources to competing projects. See the
OSCM at Work box titled “Critical Chain Project Management” for Goldratt’s ideas on
scheduling projects.
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Supply and Demand Planning and Control
Section 4
OSCM AT WORK
Critical Chain Project Management
Critical Chain Project Management is the name of the
approach that Eli Goldratt developed for scheduling and
managing projects. The approach borrows many ideas from
those used for manufacturing processes. The conventional
critical path method was covered in Chapter 4, and Goldratt
goes beyond those ideas by considering resource constraints and special time buffers in the project. The following are specific ideas included in his Critical Chain Project
Management approach:
1. Schedules are level-loaded based on the limitations of
available resources (constraints). This produces the “critical
chain”—the longest set of sequential tasks (due to both task
dependency and resource contention)—which dictates the
shortest overall project duration.
2. Time buffers are inserted at strategic locations in the plan—
at the end of the critical chain and at every point where a
task enters the critical chain—to absorb the adverse effects
of uncertainty without damaging performance. To create the
buffers, some of the slack time built into tasks in planning is
repositioned to these strategic locations.
3. Projects are “pipelined” or staged based on resource
availability to combat the cascade effect of shared
resources across projects and create viable multiproject
plans.
4. Buffer management is used to dynamically set task priorities
in execution. As uncertainty changes the original plan,
tasks are prioritized based on the buffer burn rate (the
amount of buffer consumed versus the percentage of the
work complete). Tasks with critical buffer penetration take
precedence over those with lower burn rates.
COMPARING SYNCHRO NOUS MANUFACTURING (TOC) TO
TRAD I TI ONAL APPROACHES
LO 23–3
Compare TOC to
conventional approaches.
M RP a nd JIT
MRP uses backward scheduling after having been fed a master production schedule. MRP
schedules production through a bill of materials explosion in a backward manner—working
backward in time from the desired completion date. As a secondary procedure, MRP, through
its capacity resource planning module, develops capacity utilization profiles of workcenters.
When workcenters are overloaded, either the master production schedule must be adjusted or
enough slack capacity must be left unscheduled in the system so that work can be smoothed
at the local level (by workcenter supervisors or the workers themselves). Trying to smooth
capacity using MRP is so difficult and would require so many computer runs that capacity
overloads and underloads are best left to local decisions, such as at the machine centers. An
MRP schedule becomes invalid just days after it was created.
The synchronous manufacturing approach uses forward scheduling because it focuses on
the critical resources. These are scheduled forward in time, ensuring that loads placed on
them are within capacity. The noncritical (or nonbottleneck) resources are then scheduled to
support the critical resources. This can be done backward to minimize the length of time that
inventories are held. This procedure ensures a feasible schedule. To help reduce lead time and
work-in-process, in synchronous manufacturing the process batch size and transfer batch size
are varied—a procedure that MRP is not able to do.
Comparing JIT to synchronous manufacturing, JIT does an excellent job of reducing lead
times and work-in-process, but it has several drawbacks:
1.
2.
3.
4.
5.
JIT is most often used in repetitive manufacturing environments.
JIT requires a stable production level (usually about a month long).
JIT does not allow very much flexibility in the products produced. (Products must be
similar with a limited number of options.)
JIT still requires work-in-process when used with kanbans so that there is “something
to pull.” This means that completed work must be stored on the downstream side of
each workstation to be pulled by the next workstation.
Vendors need to be located nearby because the system depends on smaller, more frequent deliveries.
Theory of Constraints
Chapter 23
Because synchronous manufacturing uses a schedule to assign work to each workstation,
there is no need for more work-in-process other than that being worked on. The exception is
for inventory specifically placed in front of a bottleneck to ensure continual work, or at specific points downstream from a bottleneck to ensure flow of product.
Concerning continual improvements to the system, JIT is a trial-and-error procedure
applied to a real system. In synchronous manufacturing, the system can be programmed and
simulated on a computer because the schedules are realistic (can be accomplished) and computer run time is short.
Re la t ion s hip with Othe r F u n ctio n al Areas
The production system must work closely with other functional areas to achieve the best operating system. This section briefly discusses accounting and marketing—areas where conflicts
can occur and where cooperation and joint planning should occur.
A c c o u n t i n g ’ s I n f l u e n c e Sometimes we are led into making decisions to suit the
measurement system rather than to follow the firm’s goals. Consider the following example:
Suppose that two old machines are currently being used to produce a product. The processing
time for each is 20 minutes per part and, because each has the capacity of three parts per hour,
they have the combined capacity of six per hour, which exactly meets the market demand
of six parts per hour. Suppose that engineering finds a new machine that produces parts in
12 minutes rather than 23. However, the capacity of this one machine is only five per hour,
which does not meet the market demand. Logic would seem to dictate that the supervisor
should use an old machine to make up the lacking of one unit per hour. However, the system
does not allow this. The standard has been changed from 20 minutes each to 12 minutes each
and performance would look very bad on paper because the variance would be 67 percent
[(20 – 12)/12] for units made on the old machines. The supervisor, therefore, would work the
new machine on overtime.
P r o b l e m s i n C o s t A c c o u n t i n g M e a s u r e m e n t s Cost accounting is used
for performance measurement, cost determinations, investment justification, and inventory
valuation. Two sets of accounting performance measurements are used for evaluation:
(1) global measurements, which are financial statements showing net profit, return on
investment, and cash flow (with which we agree); and (2) local cost accounting measurements
showing efficiencies (as variances from standard) or utilization rate (hours worked/hours
present).
From the cost accounting (local measurement) viewpoint, then, performance has traditionally been based on cost and full utilization. This logic forces supervisors to activate their
workers all the time, which leads to excess inventory. The cost accounting measurement system also can instigate other problems. For example, attempting to use the idle time to increase
utilization can create a bottleneck, as we discussed earlier in this chapter. Any measurement
system should support the objectives of the firm and not stand in the way. Fortunately, the cost
accounting measurement philosophy is changing.
M a r k e t i n g a n d P r o d u c t i o n Marketing and production should communicate and
conduct their activities in close harmony. In practice, however, they act very independently.
There are many reasons for this. The difficulties range from differences in personalities and
cultures to unlike systems of merits and rewards in the two functions. Marketing people
are judged on the growth of the company in terms of sales, market share, and new products
introduced. Marketing is sales oriented. Manufacturing people are evaluated on cost and
utilization. Therefore, marketing wants a variety of products to increase the company’s
position, whereas manufacturing is trying to reduce cost.
Data used for evaluating marketing and manufacturing are also quite different. Marketing
data are “soft” (qualitative); manufacturing data are “hard” (quantitative). The orientation and
experiences of marketing and production people also differ. Those in marketing management
have likely come up through sales and a close association with customers. Top manufacturing
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managers have likely progressed through production operations and therefore have plant performance as a top objective.
Cultural differences also can be important in contrasting marketing and manufacturing
personnel. Marketing people tend to have a greater ego drive and are more outgoing. Manufacturing personnel tend to be more meticulous and perhaps more introverted (at least less
extroverted than their marketing counterparts).
The solution to coping with these differences is to develop an equitable set of measurements to evaluate performance in each area and to promote strong lines of communication so
they both contribute to reaching the firm’s goals.
THEORY OF CONSTRAINTS—PROBLEMS ABOUT WHAT TO
PRO D UCE
LO 23–4
Evaluate bottleneck
scheduling problems by
applying TOC principles.
We now present three examples to show that different objectives and measurement criteria
can lead to the wrong decisions. These examples also show that, even though you may have
all the data required, you still may not be able to solve the problem—unless you know how!
EXAMPLE 23.1: What to Produce?
In this first example, three products (A, B, and C) are sold in the market at $50, $75, and
$60 per unit, respectively. The market will take all that can be supplied.
Three workcenters (X, Y, and Z) process the three products as shown in Exhibit 23.14.
Processing times for each workcenter also are shown. Note that each workcenter works on all
three products. Raw materials, parts, and components are added at each workcenter to produce each product. The per unit cost of these materials is shown as RM.
Which product or products should be produced?
exhibit 23.14
Prices and Production Requirements for Three Products and Three
Workcenters
Product A
$50
Product B
$75
Product C
$60
Workcenter Z
5 min./part
Workcenter X
6 min./part
Workcenter X
4 min./part
Selling price
RM
$10
Workcenter X
4 min./part
RM
$4
Workcenter Y
3 min./part
Workcenter Y
3 min./part
RM
$5
RM
$18
Workcenter Y
10 min./part
RM
$6
RM
$15
RM
$30
Workcenter Z
5 min./part
Workcenter Z
2 min./part
RM
$12
RM = Added raw materials, components, and parts
There is only one of workcenter X, Y, and Z.
RM
$20
Theory of Constraints
Chapter 23
SOLUTION
Three different objectives could exist that lead to different conclusions:
1. Maximize sales revenue because marketing personnel are paid commissions based on
total revenue.
2. Maximize per unit gross profit.
3. Maximize total gross profit.
In this example, we use gross profit as selling price less materials. We also could include
other expenses such as operating expenses, but we left them out for simplicity. (We include
operating expenses in our next example.)
Objective 1: Maximize sales commission. Sales personnel in this case are unaware of the
processing time required so, therefore, they will try to sell only B at $75 per unit and none of
A or C. Maximum revenue is determined by the limiting resource as follows:
Limiting
Resource
Time
Required
A
Y
B
X
C
Z
Product
Number Produced
per Hour
Selling
Price
Sales Revenue
per Hour
10 min
6
$50
$300
6 min
10
75
750
5 min
12
60
720
Objective 2: Maximize per unit gross profit.
(1)
Product
(2)
Selling
Price
(3)
Raw
Material Cost
(4)
Gross Profit
per Unit (2) − (3)
A
$50
$20
$30
B
$75
$60
$15
C
$60
$40
$20
The decision would be to sell only Product A, which has a $30 per unit gross profit.
Objective 3: Maximize total gross profit. We can solve this problem by finding either total
gross profit for the period or the rate at which profit is generated. We use rate to solve the
problem both because it is easier and because it is a more appropriate measure. We use profit
per hour as the rate.
Note that each product has a different workcenter that limits its output. The rate at which
the product is made is then based on this bottleneck workcenter.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Product
Limiting
Work
Center
Processing
Time per Unit
(Minutes)
Product
Output Rate
(per Hour)
Selling
Price
Raw
Material
Cost
Profit
per Unit
Profit
per Hour
(4) × (7)
A
Y
10
6
$50
$20
$30
$180
B
X
6
10
75
60
15
150
C
Z
5
12
60
40
20
240
From our calculations, and if we only consider a single product, Product C provides the
highest profit of $240 per hour. Note that we get three different answers:
1. We choose B to maximize sales revenue.
2. We choose A to maximize profit per unit.
3. We choose C to maximize total profit.
Choosing Product C is obviously the correct answer for the firm if we restrict ourselves to
making a single product. Profit can be improved to $280/hour by producing a mix of A-3,
B-2, and C-8 units each hour. This solution can be obtained by solving the “product mix”
problem described in Appendix A (see Example A.1).
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Section 4
In this example, all workcenters were required for each product and each product had a different workcenter as a constraint. We did this to simplify the problem and to ensure that only
one product would surface as the answer. If there were more workcenters or the same workcenter constraint in different products, the problem could still easily be solved using linear
programming (as in Appendix A).
EXAMPLE 23.2: How Much to Produce?
In this example, shown in Exhibit 23.15, two workers are producing four products. The plant
works three shifts. The market demand is unlimited and takes all the products that the workers can produce. The only stipulation is that the ratio of products sold cannot exceed 10 to 1
between the maximum sold of any one product and the minimum of another. For example, if
the maximum number sold of any one of the products is 100 units, the minimum of any other
cannot be fewer than 10 units. Workers 1 and 2, on each shift, are not cross-trained and can
work only on their own operations. The time and raw material (RM) costs are shown in the
exhibit, and a summary of the costs and times involved is on the lower portion of the exhibit.
Weekly operating expenses are $3,000.
What quantities of A, B, C, and D should be produced?
SOLUTION
As in the previous example, there are three answers to this question, depending on each of the
following objectives:
1. Maximize revenue for sales personnel, who are paid on commission.
2. Maximize per unit gross profit.
exhibit 23.15
Selling price
The Production Requirements and Selling Price of Four Products
Product A
$30
Product B
$32
Product C
$30
Product D
$32
Worker 1
5 minutes/unit
Worker 1
5 minutes/unit
Worker 1
5 minutes/unit
Worker 1
5 minutes/unit
RM
$3
Worker 1
10 minutes/unit
RM
$7
RM
$3
Worker 2
10 minutes/unit
Worker 2
20 minutes/unit
RM
$5
RM
$7
RM
$5
RM
$10
RM = Raw materials
Processing time per unit
Product
A
B
C
D
Selling price
Worker 1
Worker 2
$30 (each)
32
30
32
15 min.
15
5
5
20 min.
20
30
30
Raw material
cost per unit
$18
22
18
22
One Worker 1 and one Worker 2 operate on each shift. Three shifts. Five days per week. Eight hours per shift. Operating expenses $3,000 per week.
Theory of Constraints
Chapter 23
3. Maximize the utilization of the bottleneck resource (leading to maximum gross
profit).
Objective 1: Maximize sales commission on sales revenue. Sales personnel prefer to sell B
and D (selling price $32) rather than A and C (selling price $30). Weekly operating expenses
are $3,000.
The ratio of units sold will be: 1A : 10B : 1C : 10D.
Worker 2 on each shift is the bottleneck and therefore determines the output. Note that if
this truly is a bottleneck with an unlimited market demand, this should be a seven-day-perweek operation, not just a five-day workweek.
5 days per week × 3 shifts × 8 hours × 60 minutes = 7,200 minutes per week available
Worker 2 spends these times on each unit:
A
20 minutes B
20 minutes C
30 minutes D 30 minutes
The ratio of output units is 1 : 10 : 1 : 10. Therefore,
1x​​(​20​)​+ 10x​​(​20​)​+ 1x​​(​30​)​+ 10x​​(​30​)​ = 7, 200
​
550x​ = 7, 200​
x = 13.09
Therefore, the numbers of units produced are
​A = 13 B = 131 C = 13 D = 131​
Total revenue is
​13​​(​30​)​+ 131​​(​32​)​+ 13​​(​30​)​+ 131​​(​32​)​= $9, 164 per week​​
For comparison with Objectives 2 and 3, we will compute gross profit per week.
Gross profit per week (selling price less raw material less weekly expenses) is
​ 13​​(​30 − 18​)​+ 131​​(​32 − 22​)​+ 13​​(​30 − 18​)​+ 131​​(​32 − 22​)​− 3, 000
​
​
= 156 + 1, 310 + 156 + 1, 310 − 3, 000​
​
= (​ ​$68​)​loss
Objective 2: Maximize per unit gross profit.
Gross Profit
=
Selling Price
−
Raw Material Cost
A
12
=
30
−
18
B
10
=
32
−
22
C
12
=
30
−
18
D
10
=
32
−
22
A and C have the maximum gross profit, so the ratio will be 10 : 1 : 10 : 1 for A, B, C, and
D. Worker 2 is the constraint and has
​5 days × 3 shifts × 8 hours × 60 minutes = 7,200 minutes available per week​​
As before, A and B take 20 minutes, while C and D take 30 minutes. Thus
10x​​(​20​)​+ 1x​​(​20​)​+ 10x​​(​30​)​+ 1x​​(​30​)​ = 7, 200
​
550x​ = 7, 200​
x = 13
Therefore, the number of units produced is
​A = 131 B = 13 C = 131 D = 13​
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Section 4
Gross profit (selling price less raw materials less $3,000 weekly expense) is
​ 131​​(​30 − 18​)​+ 13​​(​32 − 22​)​+ 131​​(​30 − 18​)​+ 13​​(​32 − 22​)​− 3, 000
​
​​
= 1, 572 + 130 + 1, 572 + 130 − 3, 000​
​
= $404 profit
Objective 3: Maximize the use of the bottleneck resource, Worker 2. For every hour Worker
2 works, the following numbers of products and gross profits result.
(1)
Product
(2)
Production
Time
(3)
Units Produced
per Hour
(4)
Selling Price
Each
(5)
Raw Material
Cost per Unit
(6)
Gross Profit per Hour
(3) × [(4) − (5)]
A
20 minutes
3
$30
$18
$36
B
20
3
32
22
30
C
30
2
30
18
24
D
30
2
32
22
20
Product A generates the greatest gross profit per hour of Worker 2 time, so the ratio is 10 : 1
: 1 : 1 for A, B, C, and D.
Available time for Worker 2 is the same as before:
​3 shifts × 5 days × 8 hours × 60 minutes = 7,200 minutes​​
Worker 2 should produce 10 As for every 1 B, 1 C, and 1 D. Worker 2’s average production
rate is
10x​​(​20​)​+ 1x​​(​20​)​+ 1x​​(​30​)​+ 1x​​(​30​)​ = 7, 200
​
280x​ = 7, 200​
x = 25.7
Therefore, the number of units that should be produced is
​A = 257 B = 25.7 C = 25.7 D = 25.7​
Gross profit (price less raw materials less $3,000 weekly expenses) is
257​(​ ​30 − 18​)​+ 25.7​(​ ​32 − 22​)​+ 25.7​(​ ​30 − 18​)​+ 25.7​(​ ​32 − 22​)​− 3, 000
​
​
= 3, 084 + 257 + 308.4 + 257 − 3, 000​
= $906.40
In summary, using three different objectives to decide how many of each product to make
gave us three different results:
1. Maximizing sales commission resulted in a $68 loss in gross profit.
2. Maximizing gross profit gave us a profit of $404.
3. Maximizing the use of the capacity-constrained worker gave us the best gross profit:
$906.40.
Both examples demonstrate that production and marketing need to interact. Marketing
should sell the most profitable use of available capacity. However, to plan capacity, production needs to know from marketing what products could be sold.
Theory of Constraints
Chapter 23
EXAMPLE 23.3: TOC Applied to Bank Loan Application Processing3
In this example, Goldratt’s Theory of Constraints five-step approach (see Exhibit 23.2) to
removing bottlenecks is applied to a bank loan application process. As can be seen through
the example, the ideas can be applied to all types of applications, including service processes.
Step 1: Identify the system constraint. Assume that the bank is a private-sector institution and that its goal is to make more money now and in the future. Furthermore, suppose that the initial constraint is internal, namely, the loan officers are unable to carry
out all of their responsibilities in a timely manner. That is, given the current demand for
bank loan application processing, the loan officers are unable to perform all of the steps
in the loan approval process in a responsive manner that is viewed as satisfactory by its
customers.
Step 2: Decide how to exploit the system constraint. Once a constraint is identified,
management must effectively maximize the usage of the constraint’s capacity and capability to fulfill the system’s goal. By calculating the throughput yield per unit of time at the
constraining resource, management has the information necessary to prioritize the work
performed at the constraint. For example, the loan department manager could measure the
throughput yield associated with each hour spent working on each type of loan request,
such as home mortgage, automobile, and small business. The sequence of loans processed
at the constraint would then be established by the “profitability” of the different types of
loans so that the bank’s goal can be expeditiously met. An optional approach to exploitation
that complements prioritization is assuring that the constraint is always being effectively
utilized. Thus, it may be possible to redesign the loan approval process so that some of the
loan officers’ current workload is offloaded to available personnel who are currently only
being partially utilized.
Step 3: Subordinate everything else to the preceding decisions. Subordination involves
aligning all of the nonconstraint resources in support of maximizing the performance of the
constraint resource. In this case, the bank management would want to schedule appointments
for potential customers seeking to complete their loan applications with bank agents so that
there was always an abundant supply of completed loan requests waiting for the loan officers
to process. Also, the manager of the bank’s loan approval process would control the release
of loan applications into the approval process so that the loan officers were not overwhelmed.
Finally, the bank would have a non–fully occupied clerk assure that each application was
complete and met process quality standards prior to being given to the loan officers. (Note
that having a supply of finished applications available assured a highly productive usage of
loan officer time; this approach to subordination would produce only a small increase in
throughput. It would move the bank toward its goal; the constraint would remain with the
loan officers.)
Step 4: Elevate the constraint. Elevating the constraining resource means adding enough
new capacity so that the current constraint no longer limits system throughput. In contrast
to the previous two steps, elevation often requires a monetary outlay or investment for new
resources or capabilities. In the bank’s loan subsystem illustration, despite increases in loan
officer productivity that were presumed to result from steps 2 and 3, the system constraint has
remained with the bank’s loan officers. Thus, because these improvements were insufficient
to break the constraint, it is necessary to address the constraining factor directly. The obvious
step is to hire an additional loan officer. This action elevates the existing constraint by providing more than sufficient capacity to meet existing demand for processing loan applications.
While this decision would produce a sizable increase in operating expenses, it could be justified by management as the best approach to meeting their process goal as well as the bank’s
overall goal.
Step 5: Return to step 1, but do not allow inertia to cause a system constraint. After the
original constraint has been overcome in step 4, it is necessary to revisit all of the changes
made in steps 2 and 3 to determine if they are still appropriate to effective process and
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system performance. In the loan example, a review of the implemented changes in step 2
might show that offloading the responsibilities for assembling the loan package and some
of the credit checking activities to bank clerical personnel was working well and that there
is no need to go back to the original procedure. With regard to step 3, although the bank
might still seek to aggressively schedule bank agents to meet with customers to help them
complete their loan applications, it might not be possible to have a large inventory of loan
requests in progress because the constraint in the loan application and approval process had
shifted to the marketplace. Thus, it is appropriate to return to step 1 of the five-step focusing
process.
Extending the process. Exhibit 23.16 shows how the application of the five-step focusing process might realistically unfold in managing the bank’s loan application process
over the next couple of years. Elevating the capacity of the original approval process
constraint by hiring a new loan officer leads to a new constraint. This time it resides in the
marketplace. Suppose this new constraint turns out to be a policy constraint, namely, bank
management does not extend consumer loans to clients who do not use the bank’s credit
card services. Reconsideration of this policy leads to an exemption for a bank customer
who has had any type of an account at the bank for at least the past year. Next, because
there are insufficient monetary reserves to fund all of the approved loads, the new system
constraint resides in the supply of capital. To address this new constraint, assume that the
bank negotiates for additional funds from a wholesale lender and is now able to provide
more loans than customers are currently demanding. Now, a new market constraint develops because the monetary supply of funds is greater than the demand in the marketplace.
With some effort, the bank marketing team is able to break this constraint by creating a
special loan product-service bundle to serve the needs of local university students. Finally
in this example, the constraint shifts back inside the bank’s loan approval process, where
the loan officers and bank clerks are unable to process applications fast enough to keep
up with demand. Bank management purchases a new software package that has been
designed to augment loan application processing and fully trains the loan officer staff and
clerical assistants on its use.
exhibit 23.16
Sequential Application of the Five-Step Focusing Process in Managing the Bank’s Loan
Subsystem
Constraint
Location
Constraint
Type
Constraint Identification
Approach to Constraint Alleviation
Bank loan
application
process
Physical
Loan officers and bank clerks are unable
to process all customer loan applications
in a timely manner.
Some loan officer tasks offloaded to clerks and
additional loan officers hired. Now sufficient capacity exists in the loan application process.
Marketplace
Policy
Current bank policy: If a loan applicant
does not have a credit card account with
the bank, then he or she is not eligible to
apply for a consumer loan.
New bank policy: Every loan applicant must have
some type of active account with the bank. Now
demand for loans increases because more potential applicants qualify.
Supply
Physical
The availability of funds is insufficient to
meet all approved customer loan requests.
Bank negotiates for additional funds from wholesale lenders. Now capital reserves are greater than
customers are demanding.
Marketplace
Policy
Loan markets are saturated relative to current loan products, and excess funds are
available to loan to qualified customers.
Bank develops new loan product designed for
local college students. Now total demand for loans
in the marketplace increases.
Bank loan
application
process
Physical
Loan officers and bank clerks are unable
to process all customer loan applications
in a timely manner.
Bank invests in the acquisition of a new software
package to facilitate loan application processing.
Now process capacity exceeds demand.
Source: Richard A. Reid, “Applying the TOC Five-Step Focusing Process in the Service Sector: A Banking Subsystem,” Managing Service
Quality 17, no. 2 (2007), pp. 209–234. Copyright © 2007 Emerald Group Publishing Ltd.
Theory of Constraints
Chapter 23
647
Concept Connections
LO 23–1 Explain the Theory of Constraints (TOC).
Summary
∙ Eli Goldratt developed his Theory of Constraints as
an alternative way to think about improving processes.
His ideas have stimulated thought by practitioners due
to their applicability to many areas, including production, distribution, and project management.
∙ His underlying philosophy is that it is essential to concentrate on system limitations imposed by capacityconstrained resources, and for a firm to make money,
it must systematically remove these limitations.
∙ He argues that, to do this, the firm must simultaneously
increase throughput, reduce inventory, and reduce
operating expenses. He argues that improving labor
productivity will not necessarily make money for the
firm, and will only do so when it increases throughput,
reduces inventory, or reduces operating expenses.
∙ Goldratt argues that trying to maintain perfectly balanced capacity leads to many problems because this
makes every resource dependent on every other. Since
statistical fluctuations are inherent in any process,
perfect balance leads to disruptions. He argues that
not capacity, but flow through the process, should be
balanced.
Key Terms
Synchronous manufacturing A production process
coordinated to work in harmony to achieve the goals of
the firm.
Throughput The rate at which money is generated by
the system through sales (Goldratt’s definition).
Inventory All the money that the system has invested in
purchasing things it intends to sell (Goldratt’s definition).
Operating expenses All the money that the system
spends to turn inventory into throughput (Goldratt’s
definition).
Productivity A measure of how well resources are used.
According to Goldratt’s definition (see Chapter 23), all
the actions that bring a company closer to its goals.
LO 23–2 Analyze bottleneck resources and apply TOC principles to controlling a process.
Summary
∙ Managing the flow through the bottlenecks is essential to the TOC synchronous manufacturing approach.
∙ Bottlenecks are identified by calculating the expected
utilization (percentage of capacity used) for each
resource.
∙ Saving time on a bottleneck resource is the only way
to increase throughput.
∙ A technique that paces work through the system
according to the speed of the bottleneck is used to
manage flow through the system.
Key Terms
Bottleneck A resource that limits the capacity or maxi-
mum output of the process.
Nonbottleneck Any resource whose capacity is greater
than the demand placed on it (Goldratt’s definition).
Capacity-constrained resource (CCR) A resource whose
utilization is close to capacity and could be a bottleneck
if not scheduled carefully (Goldratt’s definition).
LO 23–3 Compare TOC to traditional approaches.
Summary
∙ MRP uses a backward scheduling approach and is oriented toward meeting due dates and maximizing the
use of capacity.
∙ JIT pulls material based on need, but does not allow
much flexibility for changes, particularly when capacity is tight.
648
Supply and Demand Planning and Control
Section 4
∙ Synchronous manufacturing (TOC) is more flexible
and focused on maximizing flow through the system
while minimizing cost.
∙ In order for TOC to be successfully applied, the
firm must recognize how it can be in conflict with
conventional accounting and marketing/sales thought.
Traditional cost accounting is based on a goal of fully
utilizing resources and minimizing cost. This can be
in direct conflict with TOC goals, which include maximizing profit by improving throughput.
LO 23–4 Evaluate bottleneck scheduling problems by applying TOC principles.
Summary
∙ TOC can be used to schedule production. The solutions are often very different compared to those using
conventional rules such as discussed in Chapter 22.
Solved Problem
LO23–4
Here is the process flow for Products A, B, and C. Products A, B, and C sell for $20, $25,
and $30, respectively. There are only one Resource X and one Resource Y, which are used
to produce A, B, and C for the numbers of minutes stated on the diagram. Raw materials are
needed at the process steps as shown, with the costs in dollars per unit of raw material. (One
unit is used for each product.)
The market will take all that you can produce.
a. Which product would you produce to maximize gross margin per unit?
b. If sales personnel are paid on commission, which product or products would they sell
and how many could they sell?
c. Which and how many product or products should you produce to maximize gross
profit for one week?
d. From part (c), how much gross profit would there be for the week?
Selling Price
Resource X
Resource Y
$20
$25
$30
A
B
C
X
1 min./part
RM
$1
X
4 min./part
RM
$2
Y
2 min./part
3 min./part
Y
5 min./part
RM
$5
Y
3 min./part
RM
$5
RM
$2
X
RM
$9
Solution
a. Maximizing gross margin per unit:
Gross
Margin
=
Selling
Price
−
Raw
Material Cost
A
17
=
20
−
3
B
18
=
25
−
7
C
16
=
30
−
14
Theory of Constraints
649
Chapter 23
Product B will be produced.
b. Maximizing sales commission: Sales personnel would sell the highest-priced product,
C (unless they knew the market and capacity limitations). If we assume the market
will take all that we can make, then we would work 7 days/week, 24 hours/day. Y is
the constraint in producing C. The number of C we can make in a week is
24 hours/day × 7 days/week × 60 minutes/hour
​C = ______________________________________
​
​
5 minutes/part
= 2, 016 units​
c. To maximize profit, we need to compare profits per hour for each product:
(1)
(2)
(3)
(5)
(6)
(7)
Production
Time on
Resource
(4)
Number
of Units
Output
per Hour
Product
Constraint
Resource
Selling
Price ($)
RM
Cost ($)
Gross Profit
per Hour
(4) × (5 − 6)
A
B
Y
2
30
20
3
$510
X
4
15
25
7
270
C
Y
5
12
30
14
192
If the constraining resource were the same for all three products, our problem would be solved
and the answer would be to produce just A, and as many as possible. However, X is the constraint for B, so the answer could be a combination of A and B. To test this, we can see that
the value of each hour of Y while producing B is
minutes/hour ​× ​ ​$25 − 7​ ​= $360 / hour​
______________
​​  60
(
)
3 minutes/unit
This is less than the $510 per hour producing A, so we would produce only A. The number of
units of A produced during the week is
60 minutes/hour × 24 hours/day × 7 days/week
______________________________________
​​
​ = 5, 040​
2 minutes/unit
d. Gross profit for the week is 5,040 × $17 = $85,680.
Discussion Questions
LO 23–1
LO 23–2
1. How does Goldratt’s Theory of Constraints (TOC) differ from other current approaches
to continuous improvement in organizations? How is it similar?
2. State the global performance measurements and operational performance measurements
and briefly define each. How do these differ from traditional accounting measurements?
3. Most manufacturing firms try to balance capacity for their production sequences. Some
believe this is an invalid strategy. Explain why balancing capacity does not work.
4. Individually or in a small group, examine your own experiences either working in a company or as a customer of a company. Describe an instance where TOC was successfully
applied to improve a process, or where you saw the potential for TOC to improve the
process.
5. Discuss why transfer batches and process batches often may not and should not be equal.
6. Discuss process batches and transfer batches. How might you determine what the sizes
should be?
7. Define and explain the cause or causes of a moving bottleneck.
8. Explain how a nonbottleneck can become a bottleneck.
9. Discuss the concept of “drum–buffer–rope.”
650
Supply and Demand Planning and Control
Section 4
LO23–3
LO23–4
10. Compare and contrast JIT, MRP, and synchronized manufacturing, stating their
main features, such as where each is or might be used, amounts of raw materials and
work-in-process inventories, production lead times and cycle times, and methods for
control.
11. Compare the importance and relevance of quality control in JIT, MRP, and synchronous
manufacturing.
12. Discuss how a production system is scheduled using MRP logic, JIT logic, and synchronous manufacturing logic.
13. Discuss what is meant by forward loading and backward loading.
14. Define process batch and transfer batch and their meaning in each of these applications:
MRP, JIT, and bottleneck or constrained resource logic.
15. From the standpoint of the scheduling process, how are resource limitations treated in
an MRP application? How are they treated in a synchronous manufacturing application?
16. What are operations people’s primary complaints against the accounting procedures
used in most firms? Explain how such procedures can cause poor decisions for the total
company.
17. As an individual or small group, visit your favorite fast-food restaurant during lunch
period. As you order, and while you are eating, observe as much of the process as you
can. Where are the bottlenecks in the system? What recommendations can you come up
with to relieve them?
18. When making decisions about what product(s) to produce in a manufacturing system,
why is it not enough to simply consider the selling prices and demands for different
items?
Objective Questions
LO23–1
LO23–2
1. What is the name of the software Goldratt developed to implement his idea of TOC?
2. What are the three financial measurements necessary to adequately measure a firm’s
performance?
3. What is the term that refers to the entire production process working in harmony to
achieve the profit goals of the firm?
4. What classic operational measurement does Goldratt redefine as “all the actions that
bring a company closer to its goals”?
5. The following production flow shows Parts O, Q, and T; Subassembly U; and the final
assembly for Product V.
M to N to O
P to Q
R to S to T
O and Q to U
U and T to V
N involves a bottleneck operation, and S involves a capacity-constrained resource. Draw
the process flow.
6. For the four basic configurations that follow, assume that the market is demanding product that must be processed by both Resource X and Resource Y for Cases I, II, and III.
For Case IV, both resources supply separate but dependent markets; that is, the number of
units of output from both X and Y must be equal.
Plans are being made to produce a product that requires 40 minutes on Resource X and
30 minutes on Resource Y. Assume that there is only one of each of these resources and
that market demand is 1,400 units per month.
How many hours of production time would you schedule for X and Y? What would
happen if both were scheduled for the same number of hours? (Answer in Appendix D)
Theory of Constraints
Case I
651
Chapter 23
Case II
Y
X
Market
Case III
Y
X
Market
Case IV
Market
Market
Market
Assembly
X
Y
X
Y
7. Following are the process flow sequences for three products: A, B, and C. There are
two bottleneck operations—on the first leg and fourth leg—marked with an X. Boxes
represent processes, which may be either machine or manual. Suggest the location of the
drum, buffer, and ropes.
Market
Final product
assembly
A
B
C
X
X
BN
BN
8. Willard Lock Company is losing market share because of horrendous due-date performance and long delivery lead times. The company’s inventory level is high and includes
many finished goods that do not match the short-term orders. Material control analysis
shows that purchasing has ordered on time, the vendors have delivered on time, and the
scrap/rework rates have been as expected. However, the buildable mix of components and
subassemblies does not generally match the short-term and past-due requirements at final
assembly. End-of-month expediting and overtime are the rule, even though there is idle
time early in the month. Overall efficiency figures are around 70 percent for the month.
These figures are regarded as too low.
You have just been hired as a consultant and must come up with recommendations.
Help the firm understand its problems. State some specific actions it should take. The
product flow is shown in the following diagram.
652
Supply and Demand Planning and Control
Section 4
Final
Assembly
Subassemblies
Knobs
Strike
plates
Trim
piece
RM
RM
RM
Cylinder
subassembly
Lock body
subassembly
RM
RM
Fabrication
Raw Material
RM
RM
9. The accompanying figure shows a production network model with the parts and processing sequences. State clearly on the figure (1) where you would place inventory; (2) where
you would perform inspection; and (3) where you would emphasize high-quality output.
Market
Final assembly
Bottleneck
10. The following production flow shows Parts E, I, and N; Subassembly O; and the final
assembly for Product P.
A to B to C to D to E
F to G to H to I
J to K to L to M to N
E and I to O
N and O to P
B involves a bottleneck operation, and M involves a CCR.
a. Draw the process flow.
b. Where would you locate buffer inventories?
c. Where would you place inspection points?
d. Where would you stress the importance of quality production?
Theory of Constraints
Chapter 23
653
11. Here are average process cycle times for several workcenters. State which are bottlenecks, nonbottlenecks, and capacity-constrained resources.
Processing time
Processing time
Setup time
Setup
Processing time
Idle
Setup Idle
Processing time
Setup
Processing time
Idle
Setup
Idle
12. The following diagram shows the flow process, raw material costs, and machine processing time for three products: A, B, and C. There are three machines (W, X, and Y) used in
the production of these products; the times shown are in required minutes of production
per unit. Raw material costs are shown in cost per unit of product. The market will take
all that can be produced.
a. Assuming that sales personnel are paid on a commission basis, which product should
they sell?
b. On the basis of maximizing gross profit per unit, which product should be sold?
c. To maximize total profit for the firm, which product should be sold?
A
$50
Selling Price
Y
B
$60
$10
LO 23–3
LO 23–4
5 min.
W
2 min.
X
1 min.
X
6 min.
W
2 min.
$20
$15
X
4 min.
Y
4 min.
W
5 min.
$10
$10
$15
$15
Y
3 min.
C
$70
$20
$30
13. How does synchronous manufacturing differ from MRP with respect to scheduling?
14. JIT is limited to what type of manufacturing environment?
15. Cost accounting logic can lead managers to keep their resources busy all the time, increasing productivity with no regard to demand. What is the negative result from this effect?
16. The solution to coping with natural differences between marketing and production functions is to do what two things?
17. The M–N plant manufactures two different products: M and N. Selling prices and weekly
market demands are shown in the following diagram. Each product uses raw materials
with costs as shown. The plant has three different machines: A, B, and C. Each performs
different tasks and can work on only one unit of material at a time.
Process times for each task are shown in the diagram. Each machine is available 2,400
minutes per week. There are no “Murphys” (major opportunities for the system to foul
up). Setup and transfer times are zero. Demand is constant.
Operating expenses (including labor) total a constant $12,000 per week. Raw materials
are not included in weekly operating expenses. (Answers in Appendix D)
a. Where is the constraint in this plant?
b. What product mix provides the highest profit?
c. What is the maximum weekly profit this plant can earn?
654
Section 4
Supply and Demand Planning and Control
Resources: A, B, C (one each)
Availability: 2,400 min./week
Operating expense: $12,000/week
Product M
$190/unit
100 units/week
Product N
$200/unit
50 units/week
C
15 min./unit
C
15 min./unit
A
20 min./unit
B
15 min./unit
RM-1
$60/unit
RM-2
$40/unit
B
15 min./unit
RM-3
$40/unit
18. A steel product is manufactured by starting with raw material (carbon steel wire)
and then processing it sequentially through five operations using machines A to E,
respectively (see following table). This is the only use that the five machines are
put to. The hourly rates for each machine are given in the table.
Operation:
1
2
3
4
5
Machine:
A
B
C
D
E
100
80
40
60
90
Hourly unit
output rate:
Consider the following questions.
a. What is the maximum output per hour of the steel product?
b. By how much would the output be improved if the output of B was increased to
90 per hour?
c. By how much would the output be improved if the output for C was increased to
50 per hour?
d. By how much would the output be improved if the output for C was increased to
70 per hour?
e. What is the effect on the system if machine A can only manage an output of 90
in one hour?
f. What is the effect on the system if machine C can only manage an output of 30
in one hour?
g. What is the effect on the system if machine B is allowed to drop to an output of
30 in one hour?
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. According to Goldratt, the goal of a firm is to do what?
2. At the operational level, Goldratt suggests that these
three measures should guide decisions.
3. The goal related to these three measures is this.
4. Goldratt argues that, rather than capacity, this should
be balanced.
5. This is any resource whose capacity is less than the
demand placed on it.
6. Goldratt suggests that a production system should be
controlled using these three mechanisms.
7. A bottleneck should have this placed in front of it to
ensure it never runs out of work.
8. A rope is used for this purpose in controlling a production system.
9. To pace the production system, this is used.
10. This is a measure of the value of inventory and the
time it stays within an area.
Answers to Practice Exam 1. Make money 2. Throughput, inventory, operating expenses 3. Increase throughput while simultaneously reducing
inventory and reducing operating expense 4. Flow 5. Bottleneck 6. Drum, buffer, and rope 7. Buffer 8. Communication 9. Drum 10. Dollar days
Special Topics
SECTION
FIVE
24. Health Care
25. Operations Consulting
I t ’s N ot J u st Applic able to
Manu fact u r ing and Se rvic e s
In this section of the book, we include chapters that
show how the operations and supply chain management (OSCM) concepts that were developed in the
rest of the book can be applied to specific industries. Concepts such as lean manufacturing, waste
elimination, value chain analysis, and all others are
applicable to all types of businesses, not just pure
manufacturing or service companies.
Many of you may be interested in jobs in the financial industry, for example. Many of the processes
used in this industry are repetitive, just like manufacturing processes. Take, for example, sending out
a mutual fund prospectus to investors. These documents need to be prepared and printed, are stored
in a warehouse with thousands of similar documents,
and are then mailed to actual and potential investors
at the proper time. Given the volume sent by a large
company, such as Fidelity Investments, this process
needs to be done quickly, in response to the needs
of investors, and efficiently. This process has manufacturing and logistics elements, and companies can
draw on the ideas studied here to minimize cost
while delivering the documents quickly.
We study two specific industries: health care
and consulting. We selected these because we
know that many of you may be interested in pursuing careers in these areas. Part of the process of
becoming a business professional is applying what
you learn in new and different ways that go beyond
the specific examples you studied in the classroom.
These chapters are designed to help you develop
this expertise.
655
24
Health Care
Learning Objectives
LO 24–1Understand health care operations and contrast these operations to manufacturing and
service operations.
LO 24–2 Exemplify performance measures used in health care.
LO 24–3 Illustrate future trends in health care.
THE INST ITUTE FOR HEALTH CARE
OPTIM IZATION
The Institute for Health Care Optimization (IHO) is dedicated to applying the tools and
methodologies that have been used in operations and supply chain management for
years to the heaIth care industry. Businesses have used tools such as queuing models and
simulation to design operations and material flow to minimize cost and maximize quality.
These same tools have not usually been applied for similar effect in the health care setting. The Institute for Health Care Optimization has been built on a multidisciplinary foundation that will bring together the science of operations management, clinical knowledge,
analytical skills, and an understanding of organizational behavior in the health care field.
IHO Variability Methodology™ services are
based on a unique three-phase approach for
patient flow redesign for hospitals and other
health care delivery organizations: Phase 1—­
Separate homogenous groups, such as elective
versus nonelective and inpatient versus outpatient flows. The purpose is to reduce waiting times
for urgent/emergency cases, increase throughput
in the operating rooms and cath labs, decrease
overtime, and decrease delays for scheduled
cases. Phase 2—Smooth the flow of electively
scheduled cases by decreasing the competition
between unscheduled emergency procedures
and elective scheduled procedures. The goal is
to increase hospital-wide throughput, achieve
consistent nurse-to-patient staffing, and increase
© Image Source/Jupiterimages RF
656
patient placement in appropriate units. Phase 3—Estimate resource (e.g., beds, ORs,
MRIs, staff) needs for each type of flow to ensure the right care at the right time and
place for every patient.
Source: From the Institute for Health Care Optimization Website: www.ihoptimize.org.
A hospital is a combination care facility, hotel, restaurant, and store staffed by
highly skilled professionals supported by semiskilled and low-skilled workers,
using state-of-the-art technology and employing precise discipline to perform
work of zero-defect quality on a heterogeneous population, all while trying to be
affordable.
It’s not easy . . .
Health care is the most intensive of service industries in the range of service activities and the
impact these activities have on the customer. Nowhere is this more evident than in a hospital,
where operational excellence is central to the clinical treatment of patients, the quality of their
experience, and, of course, cost. This is particularly critical in the United States, where more
than $2 trillion is spent on health care each year. It’s not just high cost alone—recent surveys
show that more than 55 percent of all Americans said they were dissatisfied with the quality
of health care. Nevertheless, numerous health care organizations are innovative and excel in
their operations performance. In this chapter, we will discuss some of the unique features of
hospitals and health care centers and how OSCM concepts and tools are used to achieve outstanding results in this critical service industry.
THE NATURE OF HEALTH CARE OPERATIONS
Health care operations management may be defined as the design, management, and
improvement of the systems that deliver health care services. Health care as a service is characterized by extensive customer contact, a wide variety of providers, and literally life or death
as potential outcomes.
The focus of our discussion of health care operations is the hospital, although everything
here is also applicable to the smaller health care clinic. The standard definition of a hospital
is a facility whose staff provides services relating to observation, diagnosis, and treatment to
cure or lessen the suffering of patients. Observation involves studying patients and conducting tests to arrive at a diagnosis; diagnosis is the medical expert’s explanation of the cause
of a patient’s symptoms; and treatment is the course of action to be followed based upon the
diagnosis. All of the services provided in a hospital are generally organized around at least
one of these three areas.
The following are important factors that set hospitals’ operations apart from other
organizations:
∙
∙
The key operators in the core processes are highly trained professionals (medical specialists) who generate requests for service (orders) but are also involved in delivering
the service.
The relationship between the prices that can be charged and actual performance is not
as direct as in most other production environments. Quality and service measures are
largely based on opinion rather than hard evidence.
LO 24–1
Understand health care
operations and contrast
these operations to
manufacturing and service
operations.
Health care operations
management
The design, management,
and improvement of
the systems that create
and deliver health care
services.
Hospital
A facility whose staff
provides services relating
to observation, diagnosis,
and treatment to cure or
lessen the suffering of
patients.
657
658
Special Topics
Section 5
∙
∙
∙
Hospitals do not have a simple line of command, but are characterized by a delicate
balance of power between different interest groups (management, medical specialists,
nursing staff, and referring doctors), each of them having ideas about what should be
targets for operations performance.
Production control approaches presuppose complete and explicit specifications of end
product requirements and delivery requirements; in hospitals product specifications are
often subjective and vague.
Hospital care is not a commodity that can be stocked; the hospital is a resource-oriented
service organization.
Cla s s ifica t io n o f Ho sp itals
The American Hospital Association classifies hospitals as follows:
∙
∙
∙
∙
General hospital/emergency room—Provides a broad range of services for multiple
conditions.
Specialty—Provides services for a specific medical condition; for example, cardiology
(heart conditions).
Psychiatric—Provides care for behavioral and mental disorders.
Rehabilitation—Provides services focused on restoring health.
As in other industries, the complexity of hospital operations has a major impact on performance. In Exhibit 24.1, we have arrayed these four types of hospitals in a product–process
framework matching range of health care product lines with complexity of operations. The
inherent complexity of general hospitals is magnified by their need for physical size and
extensive technology to handle a wide range of patient needs. Chris Hani Baragwanath Hospital is the largest hospital in the world, occupying 173 acres, with 3,200 beds and 6,760 staff
members. The hospital is in the Soweto area of Johannesburg, South Africa. Specialty hospital facilities may be large as well, but they tend to have a narrower range of medical skills
and technology onsite. An example would be the Johns Hopkins Hospital in Baltimore, which
focuses on cancer patients. Psychiatric hospitals are in a sense specialty hospitals, but because
their clinical focus is on the mind rather than the body, they are generally less technologyintense than those focusing on physical illnesses. An example of a psychiatric hospital is
McLean Hospital, affiliated with Harvard University. It is well known for its patient list of
famous people. Rehabilitation facilities are seen as least complex because, although they use
technology, the type of work done is more custodial compared to the active treatment found in
other hospitals. Veterans Administration hospitals are representative of this category.
exhibit 24.1
Hospital Product–Process Framework
Wide
General
Hospital/Emergency
Room
Range of
Products
Offered
Specialty
Hospital
Psychiatric
Hospital
Rehabilitation
Hospital
Narrow
High
Complexity of Operations
Variety of Technologies and Skills Required
Low
Health Care
Chapter 24
659
H o s p it a l La yout a nd Care C h ain s
The layout sets the physical constraints on a hospital’s operations. The goal of hospital layout
is to move patients and resources through the units and floors to minimize wait and transport
times. The layout can be determined using software models that minimize the total combined
costs of travel of patients and staff. For those situations where the numerical flow of patients
and staff does not reveal quantitative factors, manual methods such as systematic layout planning (discussed in the layout chapter) may be more appropriate.
A general rule for the design of a hospital is to separate patient and guest traffic flows from
staff flows. Use of separate elevators and dedicated resource corridors is particularly important in avoiding congestion and delays. The principal element of the overall layout of a hospital is the nursing station, which is the area support staff work from. Many nursing stations
are located in the hospital to support the various patient areas. Nursing stations today tend to
be more compact shapes than the elongated rectangles of the past. Compact rectangles, modified triangles, or even circles have been used in an attempt to shorten the distance between the
nursing station and the patient’s bed. The choice depends on such issues as the organization of
the nursing program, number of beds to a nursing unit, and number of beds to a patient room.
The growth of more holistic, patient-centered treatment and environments is leading to modifications in layout to include providing small medical libraries and computer terminals so
patients can research their conditions and treatments, and locating kitchens and dining areas
in patient units so family members can prepare food for patients and families to eat together.
The flow of work through a hospital is sometimes referred to as a care chain, consisting of
the services for patients provided by various medical specialties and functions, within and
across departments. Exhibit 24.2 lists typical characteristics of care chain processes for key
patient groups within general surgery. A major distinction among health care processes shown
in the exhibit is the extent to which access to medical treatment and resources can be scheduled efficiently. Emergency situations such as trauma must be dealt with immediately, require
rapid access to medical staff, and, as a result, are inherently inefficient. Elective procedures,
on the other hand, can be scheduled to achieve more efficient use of resources. The number of
steps, the time of each step, and whether the care chain has a definite end affects resource use
and schedule complexity. A chronic condition, for example, may lack a clearly identifiable
ending. Complexity is also increased by the need for rapid diagnostics, extensive consultation,
and the need to work with other specialties. Decoupling points are steps in the process where
waiting takes place, either before or after the procedure is performed. For many operations, it
is after diagnosis; for trauma cases, it might be after the emergency treatment and when the
patient is transferred from the recovery room to a ward.
A work flow diagram of a care chain is shown in Exhibit 24.3. It focuses on the contacts between the patient and the provider for surgery such as a hip replacement. The actual
flow can be lengthier, as when the patient wants a second opinion, and we have left out
ex hibit 24.2
Characteristics of Processes/Care Chain in a Typical General
Surgery Unit
Characteristic of Process/Care
Chain
Trauma Patients
Cancer (Oncology)
Patients
Joint Replacement
Patients
Emergency or elective
Emergency
Elective
Elective
Urgency
High
Moderate
Low
Volume
High
Medium
High
Short, long, or chronic treatment
Short
Chronic
Short
Diagnostic requirements
Immediate
Ongoing
Ongoing
Consultation requirements
Limited time possible
Involved
Little
Number of specialties involved
Depends on situation
Many
Few
Bottleneck
Operating room
Operating room
Operating room
Decoupling point
After surgery
Diagnosis
Diagnosis
Care chain
The flow of work through
a hospital consisting of
the services for patients
provided by various
medical specialties and
functions, within and
across departments.
Decoupling points
Stages in the process
where waiting takes place,
either before or after the
procedure is performed.
660
Section 5
exhibit 2 4.3
Appointment
Wait List
Referral by GP
and wait for
appointment
with a surgeon
Special Topics
Care Chain Diagram of Hip Replacement Surgery
First
Consultation
Lab Test
2nd Visit
First meeting
Medical tests to
Surgeon
with the surgeon
determine
discusses the
to determine if
patient’s ability
results and
surgery is needed to handle surgery advises of risks
Surgery Wait
List
Surgery
Preparation
Surgery
Postoperation
Stay at Ward
Schedule OR
Admission
to the
hospital
Procedural
decisions
Surgeon checks
on progress and
advises on
rehabilitation
Cycle Time and Cost Increasing
Legend
Queue
Operation
Patient Flow
recuperation at home. Also omitted are process flow modifications resulting from, say, the
patient’s medical tests indicating a particular issue like a drop in blood pressure. In this case,
the patient can either be processed serially by different specialties (e.g., blood pressure first
and hip replacement second), in parallel (blood pressure and hip replacement at the same time
with one specialty assisting the other), or as a team (both specialties present in the operating
room to work at the same time).
T r a c k i n g o f W o r k f l o w U s i n g R F I D Radio frequency identification uses
electronic tags that can store, send, and receive data over wireless frequencies. They are
now being used in a few of the more progressive hospitals to track the location of patients,
medical staff, and physical assets as they move through the hospital. Among the benefits
of using RFID for patient flow are improvement of the patient check-in process and tighter
links between patient and medical records. For example, RFID readers placed on doors
throughout the hospital can automatically detect patients as they pass through. With this
knowledge, clerks can determine where bottlenecks are likely to occur and redirect patients
to other treatment areas if the process is not sequence dependent. Thus, for example, rather
than waiting in the cardiology department for a cardiogram, a hip replacement patient could
be sent to X-ray for a required test where there is no waiting. With regard to physical assets,
RFID can pinpoint the location of equipment such as gurneys, portable X-ray machines,
and wheelchairs to help get them to the patient when needed. In addition, knowing where
each piece of equipment is can save hours that are spent at the end of the day conducting
“equipment round-ups.”
Ca pa city Pla n n in g
Capacity planning entails matching an organization’s resources to current and future demand.
Determination of the resource requirements is primarily a function of the number of customers in the hospital’s local market and the length of stay. Length of stay can be shortened
by technologies and process management, which can increase patient throughput. In health
care, capacity is measured in terms of multiple resources including beds, clinics, and treatment rooms; availability of physicians, nurses, and other providers, medical technologies, and
equipment such as X-ray machines; facility space such as hallways and elevators; and various
support services such as cafeteria and parking.
Health Care
Chapter 24
The starting point in developing a capacity plan is determining the effective capacity of
a resource over some period of time. This is accomplished by multiplying design capacity
(which is the capacity if the resource is operated continuously) by the average utilization rate.
The formula is
Effective capacity = Design capacity × Utilization
For example, if average utilization is 70 percent on an X-ray machine that could operate
24 hours per day, 7 days a week, then its effective capacity per day is 16.8 hours per day
(24 hours × 0.7 = 16.8 hours). It should be noted that the 70 percent utilization figure is in
line with the 70 percent utilization target common to companies seeking a high level of service. The subsequent steps consist of (1) forecasting patient demand by hour, location, specialty, and so on; (2) translating this demand, adjusted by productivity estimates, into capacity
requirements; (3) determining the current capacity level in terms of hours of staff, facilities,
and equipment; (4) calculating the gap between demand and capacity on a per-hour basis; and
(5) developing a strategy to close the gap. This can be done by several common approaches,
including transferring capacity from other units, increasing capacity through overtime, subcontracting with other hospitals, and bottleneck reduction.
Wo r k for ce S che duling
The primary areas of importance in hospital scheduling are nurse shift scheduling and operating room scheduling. Nurses constitute the largest component of the hospital’s workforce, and
operating rooms (or surgical suites) are typically the largest revenue-generating centers.
The nurse shift schedules can be classified as either permanent (cyclical) or flexible (discretionary). In cyclical scheduling, the work is usually planned for a four- to six-week period,
where employees work on a fixed schedule each week over the period (for example, the conventional fixed, five 8-hour days each week). Several types of flexible scheduling are used,
but the most popular is the flexible week, where nurses maintain 8-hour days and average
40 hours per week but can alternate between, say, 8 hours for four days and 8 hours for six
days. Both cyclical and flexible schedules have their pros and cons, though the edge seems to
go to flexible systems because they are better suited to handle fluctuations in demand, as well
as meeting the desires of nurses to change from full- to part-time. Several personnel scheduling techniques are described in Chapter 22.
Qu a lit y M a na ge m e nt a n d Pro cess Imp ro vemen t
Ever since the work of Florence Nightingale (see the OSCM at Work box later in this section), hospitals have been seeking ways to achieve quality and process improvement. TQM
approaches have been a staple for decades, and within the past few years Six Sigma and lean
concepts are being instituted in many hospitals. Hospital personnel are well suited to analytics
of TQM because so much of health care involves precise measuring of patient responses to
drugs and clinical procedures.
G a p E r r o r s a n d B o t t l e n e c k s Two problems that get frequent attention in quality
programs are dealing with gap errors and bottlenecks. Gap errors are information mistakes
that arise when a task is transferred or handed off between people or groups. Many professional
routines, such as formal handoff procedures between shifts of nurses and physicians are
designed to bridge gaps. Handoffs may be as significant a source of serious patient harm as are
medication-related events. In a study of formal handoff procedures, 94 percent of the handoffs
were conducted face-to-face, more than half of the 161 residents surveyed reported that they
were rarely done in a quiet, private setting, and over a third reported frequent interruptions.
One successful approach to managing handoffs is the SBAR (Situation-BackgroundAssessment-Recommendation) checklist technique for communicating information about
a patient’s condition between members of the health care team. Adapted from a program
used to provide quick briefings of nuclear submariners during a change in command, SBAR
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OSCM AT WORK
Florence Nightingale, Hospital Quality
Improvement Pioneer
Long before Deming, Crosby, and the other industrial quality
gurus, Britain’s Florence Nightingale was leading a quality
revolution in hospitals. During the Crimean War, the British
public was shocked by reports of the terrible conditions
of British hospitals, and Nightingale, founder of the modern profession of nursing, was sent to Scutari, Turkey, to
improve them. In addition to overseeing the introduction of
nurses to the hospitals, she also led the effort to improve
sanitary conditions in the hospitals. Central to her approach
was collecting, tabulating, interpreting, and graphically displaying data relating to process care changes on outcomes.
(She is credited as being the developer of the pie chart.)
For example, to quantify the overcrowding of hospitals, she
compared the amount of space per patient in London hospitals, 1,600 square feet, to that in Scutari, 400 square feet.
She also developed a standard statistical form to enable the
collection of data for analysis and comparison. The results
of these innovations were astounding: The mortality of
patients decreased from 42 percent in February 1855 to 2.2
percent in June of that year. Nightingale’s approach, termed
evidence-based medicine, underlies current approaches to
medical practices.
© Hulton Archive/Getty Images
is an easy-to-remember tool for framing any conversation requiring a clinician’s immediate
attention and action.
As discussed elsewhere in the book, a bottleneck is that part of the system that has the
smallest capacity relative to the demand on it. Bottlenecks frequently result from individual
departments optimizing their own throughput—the number of patients or procedures per
hour—without considering the effects on upstream or downstream departments. If changes are
made to improve parts of a system without addressing the constraint, the changes may not result
in a reduction of delays and waiting times for the entire system. To identify the constraint,
observe where the work is piling up or where lines are forming, and perform some simple calculations. For example, Exhibit 24.4 shows the capacity of the five processes in a preoperative
clinic at Beth Israel Deaconess Medical Center in Boston. (Note that nursing is the bottleneck.)
The handbook provides suggestions for eliminating bottlenecks. These are presented in
Exhibit 24.5.
S e r v i c e Q u a l i t y Hospitals, like other customer contact businesses, have been raising
the level of their customer service to improve the patient experience. This has been shown to
exhibit 24.4
Pre-op Clinical Capacity at Beth Israel Deaconess Medical Center
Anesthesia
Nursing
Phlebotomy
EXG
X-ray
Total process (minutes including
paperwork)
15
18
8
10
9
Estimated capacity (number of visits
per day) with breaks, calls, lunch
48
36
58
42
On-call
Range of visits per day (4-day period)
27−45
23−11
22−41
11−30
7−21
Average number of visits per day
(4-day period)
35
27
29
20
14
Health Care
ex hibit 24.5
Chapter 24
Diagnoses and Remedies for Eliminating Bottlenecks
How to Manage the Constraint
Diagnoses (Dxs)
Remedies (Rxs)
Constraints should not have idle
time.
The doctor is in the exam room
waiting to see the first patient of
the day while the patient is being
registered.
Register the patient after the
exam.
If experts are the constraint, they
should be doing only work for
which an expert is needed.
In preoperative testing, patients
are backed up waiting for the
nurse (the constraint in the
process).
The receptionist or assistant
assumes tasks that are being
done by the nurse but that do
not require nursing skills.
Put inspection in front of a
constraint.
On the day of the surgery, key
X-rays are not available.
One person coordinates and
expedites all necessary information on the day of the surgery.
save money through reductions in malpractice suits, reductions in no-shows, and lower nurse
turnover. The standard philosophy is an end-to-end customer focus. An example of this focus
is at Good Samaritan Hospital in Los Angeles. When patients arrive at “Good Sam” for an
appointment, rather than having to sit in a waiting room they are greeted at a modern hotel-like
lobby and escorted directly to the unit of the hospital where they are to be treated. During their
stay, efforts are made to ensure that their comfort needs are anticipated (such as having an extra
pillow in the room), and before leaving a patient, every employee is to ask, “Is there anything
else I can do for you?” In addition, hospital patients can use the Red Carpet Hospitality
Program, which provides concierge-like services such as the ordering-in of meals from local
restaurants and providing information about local accommodations and spas for families.
H e a lt h Ca r e S upply Cha in s
H o s p i t a l S u p p l y C h a i n s Exhibit 24.6 presents a hospital supply chain, showing
the flow of three essential resources: information, funds, and goods and services. Goods and
services move downstream from manufacturers to distributors/third-party logistics providers
(3PL) and retailers to the hospital warehouse to receiving to central stores, and then to
nursing and patients. Cash/funds flow upstream. On a day-to-day basis, hospital supply chain
management focuses on medical supplies and pharmaceutical supplies. Traditionally, these
activities are operated as separate organizational units. The medical-surgical supplies are
complex, and are ordered from multiple vendors and from manufacturers. For the pharmacy,
the vast majority of medications come directly from the distributors. Very few ship directly
ex hibit 24.6
Health Care Supply Chain
Goods and Services
Manufacturers
Distributors
Cash/Funds Flow
Hospital
Patients
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from the manufacturer. Current approaches involve merging of the two procurement operations
within one department to reduce the number of vendors and to get better transparency.
P h y s i c i a n - D r i v e n S e r v i c e C h a i n s The widespread use of computerized
physician order entry (CPOE) systems for prescriptions has led experts to propose broadening
their application to include scheduling all resources needed by physicians to treat their individual
patients. Called “event management,” the way it works is that the admission order for a patient—
for example, for a surgery procedure—triggers a series of follow-up events that are automatically
entered into the information system (see Exhibit 24.7). The information system then initiates an
admission date and books an operating room date, a surgical team (including an anesthesiologist
and nurses), recovery room, and lab tests. These activities and processes are linked as well. For
example, an electronically issued lab order for blood work is routed directly to the phlebotomist,
who then draws and ships blood to the lab for analysis. Lab managers use the information to
batch orders. Behind the scenes, accounting transactions are generated for billing insurance
companies, recording copayments, placing purchase orders for supplies, and so on.
Inve ntory Ma n agemen t
Diagnosis-related
groups (DRGs)
Homogeneous units
of hospital activity for
planning and costing
surgeries—essentially a bill
of labor and materials.
Average inventory for medium-size hospitals is about $3.5 million. It represents 5 to 15 percent
of current assets and 2 to 4 percent of total assets; typically, inventory is the largest working
capital requirement. The cost of inventory is directly related to the hospital’s case mix. A casemix index is calculated based on classifications such as diagnosis-related groups (DRGs).
DRGs classify patients by diagnosis or surgical procedure (sometimes including age) into
major diagnostic categories (each containing specific diseases, disorders, or procedures)
based on the premise that treatment of similar medical diagnoses generate similar costs. Over
1,000 DRGs have been developed for Medicare as part of the payment system.
Hospital inventory management systems can be broken down into two general categories:
push systems, consisting of fixed–order quantity systems and fixed–time period systems (covered in Chapter 20), and pull systems, using just-in-time delivery (covered in Chapter 14). The
basic difference between the two categories is that push systems either place reorders for a set
amount in anticipation of need (fixed–order quantity systems) or count inventory at set time periods and place orders to bring inventory to a predetermined level (fixed–time period systems). Pull
exhibit 24.7
Supply Chain Event Management
Accounting
Imaging
Purchasing
Materials
inventory
Radiology
Phlebotomist
Pharmacy
Order
Order
Order
Lab
Operating
room schedule
Order
Admission
Instructions
Recovery
Food service
Order
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systems, by contrast, have mechanisms called pull signals to supply inventory just-in-time (JIT)
for use. Push systems make sense when a hospital owns its own inventory or buys in bulk and
then breaks it down to distribute to nursing units or floors when required. JIT makes sense for
expensive items such as implants, which are supplied by a partner vendor on a pull-system basis.
A major distinction between health care inventory management and that of other businesses is planning safety stock. The standard calculation of safety stock is predicated on trading off the cost of carrying an additional unit of inventory with the cost of being out of stock.
In a department store, we can easily balance the cost of holding too many pairs of jeans with
the cost (or lost profit) caused by running out of them. In hospitals, such trade-offs are much
trickier when faced with balancing the cost of holding, say, a unit of type A blood with the
cost of running out of it. The problem with estimating the cost of a stockout in a hospital is
that consequences such as prolonged patient pain or even (though rarely) a threat to the life of
the patient may be an issue. For critical items, backup contingency plans such as borrowing
from a nearby hospital are often developed.
PER FORMANCE MEASURES
The following are typical indicators used to measure performance at a health care clinic:
∙
∙
∙
∙
Customer satisfaction—Survey rating of primary care provided and subspecialty care
provided.
Clinical productivity and efficiency—Patient visits per physician per workday.
Internal operations—Patient complaints per 1,000 patients. Patient waiting time for
appointments.
Mutual respect and diversity—Percentage of staff from underrepresented groups.
Employee satisfaction survey.
LO 24–2
Exemplify performance
measures used in health
care.
As can be seen, most of the performance indicators are tied to operations management.
Pe r for m a nce D a s hboa r ds
Current practice is to present detailed day-to-day performance measures on dashboards in
three major categories: customer service, clinical operations, and key processes. A customer
service dashboard provides such scoring information as percentage of patients who would
recommend the hospital to others and rating of such items as inpatient parking, courtesy of
staff, cleanliness, caring of staff, meal quality, follow-up education and instruction, and pain
management, as well as an overall satisfaction. A clinical dashboard measures performance
metrics such as mortality rate, quality improvement, readmission rate, and various procedurespecific key performance indicators. A key process dashboard would display, for example,
percentage of transfusions having reactions, accurate performance of transfusions protocols,
adverse drug reactions, medicine error severity, autopsy rate, employee exposures to blood
and bodily fluids, and code response times.
TREND S IN HEALTH CARE
Among the major trends in health care that relate to OSCM are the following.
Evidence-based medicine (EBM): EBM is the application of the scientific method to
evaluate alternative treatment methods and create guidelines for similar clinical situations.
Essentially, it is the development of standard methods for therapeutic interventions.
Integrated medical care: Developed by the Mayo Clinic, this approach has a number of
philosophical as well as operational features, including staff/team work with multispecialty
integration, unhurried examination with time to listen to the patient, the hospital physician
taking personal responsibility for directing patient care over time in a partnership with the
local physician, and integrated medical records with common support services for all patients.
LO 24–3
Illustrate future trends in
health care.
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OSCM AT WORK
Remote Doctor Consultation!
You broke your ankle playing tennis yesterday afternoon.
What a mess—the whole joint dislocated and three broken
bones. The doctor says that it might be a year before you
are back to normal. Your surgery was performed last night.
No pain right now, but the medication coming through that
tube connected to your arm may be the reason for that.
The doctor wanted to get the surgery done last night
since he was leaving for vacation early this morning. Just
prior to going under the knife, he assured you that everything would be fine and that he would talk to you in the
morning. He is 700 miles away by now, so how could this be?
The Remote Presence Robot (RP-7) from InTouch Health is a
mobile telemedicine unit that connects physicians and specialists
with patients and other doctors in real time through computers
equipped with cameras and microphones.
© Patrick Farrell/Miami Herald/MCT/Getty Images
The nurse comes in and asks how things are going.
She says the doctor wants to talk and asks if I am up for that.
“Sure,” I say, but I am still unsure how this can be done. “No
problem, I’ll be right in with the doctor” says the nurse. The
nurse rolls in a device like I had never seen before. It looks to
be a little over 5 feet high and has a computer monitor on top.
I hear a voice say, “Hi, how are you doing?” I look up
and sure enough there is my doctor on the screen. He tells
me about how well the surgery went. He describes how he
put a plate in my ankle and seven screws to hold everything
together. He explains that it is going to take time for all of this
to heal and that after six months he would probably do another
surgical procedure and take the plate and screws out. It is all
part of the process. He said he would check in with me again
tomorrow morning and that it might be four or five days before
I could leave the hospital. Also, I should let the nurses know if I
am feeling any pain. He assured me that he was connected to
the gadget through an app and that the nurses could contact
him quickly, even better than if he were at the local office.
This type of electronic physician assistant gives the
doctor direct access to current data related to the patient—
heart rate, blood pressure, sleep and active periods, and
current drugs being administered. In many ways, this is even
better than the old way of doing hospital rounds. Everything
is at the doctor’s finger tips; the information is in real-time
and accurate.
The “Remote Presence Robot” is a reality and is being
used by many hospitals today. Physician-to-patient communication is now possible regardless of whether a physician
is out of town or out of the country. Doctors can now make
rounds off-site or from their office any time of the day via an
app on the physician’s cell phone. Patients are still monitored
by the hospital nursing staff, but now they have a direct link to
the doctor via the app with real-time ability to communicate.
Many patients are impressed with the new technology
as it gives doctors the ability to provide better coverage to
patients, rather than everything being done face-to-face.
For example, the doctor is now able to connect and see the
patient when family members are visiting. This is so much better when the need to communicate with the family is critical.
Electronic medical records: Digital technologies are revolutionizing the way patient records
are gathered and stored. For example, emergency department doctors and nurses at Kaiser
Permanente in Oakland carry flat computer tablets that can access every patient’s entire medical record. These tablets also enable doctors and nurses to call up medical test records and
X-rays right at the patient’s bedside. Similar technologies are now within the reach of smaller
medical practices with handheld tablet PCs for medical records being sold by Walmart.
Health information exchanges (HIEs): HIEs provide the capability to electronically
move clinical information over various kinds of information systems while maintaining the
meaning of the information being exchanged. For example, the Indiana Health Information
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Exchange (IHIE) allows physicians to track in real time those patients who are due for preventive screenings and chronic disease follow-up care.
Computer-assisted diagnosis: This approach uses expert system software programs to
arrive at a diagnosis. Suppose the doctor with a child patient who has pain in the joints wants
to determine its most likely cause. The expert system matches the child’s symptoms with the
criteria tables for each type of illness and reaches diagnostic conclusions at three different
levels of certainty: definite, probable, and possible. If the diagnosis is suggested at the “possible” level, the system recommends looking for further clues to exclude or include it.
Remote diagnosis: Called telemedicine, it uses electronic devices for measuring blood
pressure, heart rate, blood oxygen levels, and so on, for diagnosing patients who are far
from the hospital. This is especially valuable in areas where few specialists are available to
rapidly diagnose a patient’s problem.
Robots: Robots are being used in the operating room for a range of illnesses that include
breast cancer and gall bladder removal. In using robots, surgeons employ a tiny camera to
guide them as they manipulate the robot’s instruments from a console. Benefits of robots
are that their “hands” are steady and they have a wide range of motions, which can result in
less pain and blood loss than with manual surgery. An interesting low-tech robotic application is Mr. Rounder, described in the OSCM at Work box.
Concept Connections
LO 24–1 Understand health care operations and contrast these operations to manufacturing and
service operations.
Summary
∙ Health care is an industry that requires operational
excellence. The focus of this discussion was hospitals,
but these ideas are also applicable to more specialized
clinics.
∙ Hospitals are categorized in a manner similar to the
way production processes are, using the product/
process matrix. Layouts, capacity management, quality and process improvement, supply chains, and
inventory, all in the context of hospitals, are described.
Key Terms
Health care operations management The design, man-
agement, and improvement of the systems that create
and deliver health care services.
Hospital A facility whose staff provides services relating to observation, diagnosis, and treatment to cure or
lessen the suffering of patients.
Care chain The flow of work through a hospital consisting of the services for patients provided by various
medical specialties and functions, within and across
departments.
Decoupling points Stages in the process where waiting takes place, either before or after the procedure is
performed.
Diagnosis-related groups (DRGs) Homogeneous units
of hospital activity for planning and costing surgeries—
essentially a bill of labor and materials.
LO 24–2 Exemplify performance measures used in health care.
Summary
∙ A diverse set of performance measures are used in
health care.
∙ In addition to traditional customer satisfaction and
worker (physician) productivity measures, other ways
to capture patient mortality, and follow-ups from the
administration of procedures, for example, may be
used.
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Section 5
LO 24–3 Illustrate future trends in health care.
Summary
∙ The application of new technologies drives change in
the health care area.
∙ The integration of information, remote and computerassisted diagnosis, and the use of remotely controlled
robots have all resulted in dramatic changes in productivity, while improving the quality of patient care.
Discussion Questions
LO24–1
LO24–2
LO24–3
1. Where would you place Shouldice Hospital on the product–process framework (see
the Chapter 5 case, “Shouldice Hospital—A Cut Above”)? What are the implications of
adding a specialty such as cosmetic surgery?
2. Think about your latest trip to a hospital/health care facility. How many different handoffs did you encounter? How would you rate the quality of the service relative to the
patient experience and relative to that of the friends and family?
3. Some have argued that, for hospitals, both medical schools and nursing schools should be
considered part of the supply chain. Do you agree?
4. Hospitals are major users of poka-yoke (fail-safe) devices. Which ones can you think of
that would apply?
5. Could a hospital or physician offer a service guarantee? Explain.
6. How does a physician-driven supply chain differ from a typical materials supply chain?
7. What could a hospital learn from benchmarking a Ritz-Carlton Hotel? Southwest Airlines? Disneyland?
8. As in manufacturing, productivity and capacity utilization are important performance
measures in health care operations. What are the similarities and differences in how these
measures might be used in the two different industries?
9. What would you consider to be the most important performance measure in a hospital?
Explain.
10. As the “baby-boomer” generation ages, the percentage of the U.S. population over age 65
will grow at a faster rate than the size of the workforce paying taxes and health insurance
premiums. How do you expect that to impact health care operations and supply chain
management?
Objective Questions
LO24–1
LO24–2
LO24–3
1. In manufacturing, quality measures are largely based on hard evidence. In health care,
what are quality and service measures largely based on?
2. A general rule of designing hospital layouts is to separate patient/visitor flow from
what? (Answer in Appendix D)
3. What is the term used to refer to the flow of work through a hospital?
4. What inventory-related term is used to refer to points in a health care process where waiting takes place, either before or after treatment takes place?
5. What type of worker constitutes the largest component of the hospital’s workforce?
6. In hospitals, dashboards are often used to display performance measures on a routine
basis. What type of dashboard tracks metrics such as mortality rate, quality improvement,
and readmission rates? (Answer in Appendix D)
7. What dashboard would display metrics such as accurate performance of transfusion protocols and code response time?
8. Remote diagnosis uses electronic devices for diagnosing patients at a distance. What is
another term used to refer to this practice?
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9. What is the term used to describe arrangements to move clinical information across various information systems while still maintaining the meaning of the information being
exchanged?
10. What is the term used to refer to the application of the scientific method to evaluate alternative treatment methods and create guidelines for similar clinical situations?
Case: Managing Patient Wait Times at a Family Clinic
You have a job assisting the Medical Director at a Family
Medical Clinic in New York City. The Medical Director
is concerned about the long wait times of patients visiting the clinic and would like to improve operations. The
following are facts about the clinic:
∙ The patients are seen in the clinic between the
hours of 9:00 A.M. and 12:00 P.M. and between 1:00
and 5:00 P.M.
∙ On average the clinic sees 150 patients per day.
∙ Nine physicians are usually on duty to see patients
at the clinic. Physicians arrive at 9:00 A.M. and are
on duty until 5:00 P.M. with a one-hour break during the day.
∙ They are supported by seven medical assistants
who take vital signs and put patients in exam
rooms.
∙ Four registration clerks are present to register
patients, enroll them in federal and local aid programs, prep their medical records, and collect
copayments.
∙ There are three coordinators who make follow-up
appointments and arrange referrals. Coordinators
see patients from 9:00 A.M. until 5:30 P.M., with a
one-hour break during the day.
∙ There is one security guard who is available from
7 A.M. to 6 P.M.
∙ There is one pharmacist, and two pharmacy technicians. The pharmacy is open from 9:00 A.M. to
5:30 P.M., with a lunch break from noon to 1:00.
∙ The facility itself has a security window at the
front door with a guard-controlled entry door, a
large waiting area, five registration windows, 11
provider rooms (3 of which are used for taking
vitals and 8 by physicians for exams), and four
coordinator’s desks.
Patient Flow Through the Clinic
An average of 120 patients have appointments at the
clinic each day. An additional 30 patients come for prescription refills each day.
Step 1—Security/Check-in
When patients arrive, they all must first pass through
security. Often, there is a small wait outside at the door.
The average wait time at security is 10 minutes, while the
average processing time is 2 minutes. The guard at the
door double-checks the appointment time and issues
the patient a colored card with a number on it—either
red or yellow. Red cards are reserved for patients without
appointments who need only medication refills. These
patients must pass through registration but do not need
to see a provider.
Step 2—Registration
All patients then proceed to the waiting room where they
wait for their color and number to be called. This wait
can often be quite long, but on average takes 24 minutes.
Once patients are called by a registration clerk, their
information is verified. This process can take anywhere
from 1 minute up to 40 minutes if the patient is new and
needs to be enrolled in several programs. On average,
eight new patients come per day. The average time to
complete registration is 7 minutes for returning patients
and 22 minutes for new patients, with an overall average
registration time of 8 minutes. Patients seeking medication refills (with red cards) proceed directly to the pharmacy (step 6) after registration.
Step 3—Vitals
The yellow card patients return to the waiting area and
wait another 15 minutes to be called by a medical assistant to have their vital signs taken. This takes 6 minutes,
after which they return again to the waiting area.
Step 4—Doctor Visit
Patients wait 8 minutes more in the waiting room and
are then called back to a provider room. Once in a provider room, the patient waits 17 minutes, on average, for
the provider (doctor) to arrive. Providers spend approximately 20 minutes with each patient.
Step 5—Coordinator/Follow-up
After the patient has seen the doctor, the patient’s chart
goes to a coordinator. The patient waits 25 minutes to be
called by a coordinator who schedules further laboratory
tests, get referrals to specialists, and makes follow-up
appointments, which takes an additional 7 minutes.
On average, 50 percent of patients with appointments
(yellow cards) continue onto the pharmacy following
their medical visit.
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Step 6—Pharmacy
If the patient needs a prescription, the wait is 13 minutes before the pharmacy calls them to process the prescription, with an average of 11 minutes spent filling
the prescription. Each pharmacy technician works independently and fills the prescription after consulting the
pharmacist.
In general, patient satisfaction with the quality of medical services at VFC remains high, but there are still complaints each day about the waiting times for these services.
Wait times are critical for these patients, because they often
directly lead to lost income during the hours spent waiting.
The Physicians’ Workflow
Each physician is assigned to a team; A, B, or C. These
groups of two or three physicians all see the same
patients, helping to ensure continuity for the patients.
Each patient, therefore, will see one of the team’s physicians at any given visit and has a higher likelihood of
seeing the same doctor each time.
Physicians arrive at 9:00 A.M. and wait for their first
patients to arrive. Often, due to the lag at registration and the
wait for open rooms for the medical assistants to take vitals,
patients are not in the exam rooms until well after 9:30.
In addition, because of the team system, one provider
may have three patients waiting, while another is still waiting for his or her first patient to check in at registration.
The registration desk has no communication link to the
physicians’ area or other form of coordination; so clerks
may check in three patients in a row for one team, but
none for another. Added to this, new patients are randomly
assigned to teams regardless of who is busiest that day.
Once a patient is in an exam room, the chart is placed in
a rack for the physician to review prior to seeing the patient.
If key lab report or X-ray results are missing, the physician
must call for medical records or call outside facilities and
wait for the results to be faxed or called in before seeing the
patient. This happens 60 to 70 percent of the time, causing
a 10-minute delay per patient. These challenges often lead
to inefficient use of the provider’s time.
After seeing a patient, the physician will either have the
patient wait in the waiting room to see the coordinator or
have the patient wait in the exam room for further testing
or nursing procedures. Rarely, if no follow-up or prescriptions are needed, the patient is free to leave the clinic.
The physicians generally are extremely committed to
the clinic’s mission but are frustrated with their patients’
long wait times, the incomplete medical records, and the
disorganized patient flow through the clinic.
The Registration Clerks’ Workflow
At the start of each day, the four registration clerks prepare
by printing out copies of that day’s scheduled appointments. Charts of patients with appointments are pulled the
night before and placed within easy reach of the clerks.
The four clerks work from 8:30 until 11:00 A.M. and close
the registration windows until 12:30 P.M. During this time,
in addition to eating lunch, the clerks pull the charts for
the afternoon clinic and finish up paperwork. At 12:30,
the registration windows are reopened for the afternoon
clinic and patients are checked in until 4:00 P.M.
Questions
1. Draw two process flow diagrams. One for the pharmacy customers, and another for the regular and
new patients.
2. Calculate the capacity and utilization of each
resource (people, rooms) and identify bottlenecks.
3. Calculate the average wait and time in service for
patients with appointments (new and returning)
and for those seeking a prescription refill.
4. What are your recommendations for improvement?
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. A hospital consists of these three basic services.
What are these?
2. The most complex type of health care facility.
3. The type of schedule where workers work on a fixed
schedule each week over a four- to six-week period.
4. The hospital quality pioneer who is credited as the
developer of the pie chart.
5. A term used to refer to information mistakes at
handoffs.
6. A checklist technique developed by submariners that
is now used in hospitals.
7. A widely used case-mix index classification scheme.
8. Use of the scientific method to develop standard
methods for therapeutic interventions.
9. The two general categories of hospital inventory
management systems.
10. A nickname for InTouch Health’s RP-6 for Remote
Presence.
11. Stage in a health care process where waiting takes
place.
Answers to Practice Exam 1. Observation, diagnosis, and treatment 2. General hospital/emergency room 3. Cyclical schedule 4. Florence Nightingale 5. Gap error 6. SBAR (Situation-Background-Assessment-Recommendation) 7. Diagnosis-related groups 8. Evidence-based medicine
9. Push systems and pull systems 10. Mr. Rounder 11. Decoupling point
Operations
Consulting
25
Learning Objectives
LO 25–1 Explain operations consulting and how money is made in the industry.
LO 25–2 Illustrate the operations analysis tools used in the consulting industry.
LO 25–3 Analyze processes using business process reengineering concepts.
PI TTI GLIO RABIN TO DD & MCGRATH
(PRTM)—A LEADING OPERATIONS
CONSULTING CO MPANY
Good business strategy plots changes in where a company is going. A winning operational strategy translates that direction into operational reality, creating strategic competitive advantage in the process. PRTM is a leading company specializing in finding
ways to structure business operations to create breakout results in top-line growth,
earnings, and valuation.
Today’s operational CEOs realize that brilliant business strategies and operational
strategies are interconnected. Business strategies drive the need for new operational
capabilities, and evolving operational capabilities shape the future business strategies.
PRTM Consultants focus on the following six essential ingredients of operational strategy:
•
Transform market forces into operational advantage. This is the kind of
insight that Black & Decker used to turn a regulatory requirement for doubleinsulated power tools into a new modular product platform that redefined cost
and performance in category after category. The same type of insight helped
Progressive Insurance transform automobile claims from an unproductive
part of its cost structure into a far more economical and valued source of
competitive advantage.
•
Do one thing extraordinarily well. Consider the case of Apple iTunes.
Its gigantic share of the digital music player market is fueled by Apple’s
relentless pursuit of ease of use as a basis of competition. Companies
like Walmart are all about cost leadership, attaining the lowest end-to-end
operational cost, and the highest productivity.
•
Think end-to-end, continuous, real time, and horizontally. Every
organization has a set of core operational domains that make up its
671
operational model. For most, these comprise some combination of the
product development chain, the supply chain, and the customer chain.
Operational strategy configures these operational domains to deliver against
business strategy, and create advantage in their own right.
•
Think and execute globally. Due to global markets for products and the
global availability of supply, many companies need to consider strategies that
best position the firm to compete in this domain. Global opportunities are
often the key driver to changes to both business and operational strategies.
•
Drive innovation in your operations and business model. Peter Drucker
defined innovation as change that creates a new dimension of performance.
He also stated that a key accountability of the CEO is innovation. Too often,
innovation is perceived to be a technical or product-oriented activity. The
reality is that operational innovation is creating the commanding leaders
today.
•
Execute relentlessly. A complete operational strategy requires a
commitment to execution. Companies with commanding leads in their
markets execute relentlessly, informed by their global marketplace insight,
and are aligned to a singular competitive focus, emboldened by a clear
innovation intent, and guided by a sound operational model aligned with
business strategy and business economics.
In the twenty-first century, companies that make all aspects of their operations a
source of strategic innovation will dominate their markets, delivering unparalleled revenue growth, earnings performance, and shareholder return.
Source: Adapted from a statement by Tom Godward and Mark Deck, partners in PRTM’s Worldwide
Operational Strategy Practice, www.prtm.com.
Operations consulting has become one of the major areas of employment for business
school graduates. The page cited from the PRTM Website nicely summarizes the importance
of operations on bottom-line performance. In this chapter, we discuss how one goes about
consulting for operations, as well as the nature of the consulting business in general. We also
survey the tools and techniques used in operations consulting and provide an overview of business process reengineering because much OSCM consulting entails this activity.
WHAT I S OPERATIO NS CONSULTING?
LO 25–1
Explain operations
consulting and how money
is made in the industry.
Operations consulting
Assisting clients in
developing operations
strategies and improving
production processes.
672
Operations consulting deals with assisting clients in developing operations strategies and
improving production processes. In strategy development, the focus is on analyzing the capabilities of operations in light of the firm’s competitive strategy. It has been suggested that market
leadership can be attained in one of three ways: through product leadership, through operational
excellence, or through customer intimacy. Each of these strategies may well call for different
operations capabilities and focus. The operations consultant must be able to assist management
in understanding these differences and be able to define the most effective combination of technology and systems to execute the strategy. In process improvement, the focus is on employing
analytical tools and methods to help operating managers enhance performance of their departments. Deloitte & Touche Consulting lists the actions to improve processes as follows: refine/
Operations Consulting
Chapter 25
673
revise processes, revise activities, reconfigure flows, revise policies/procedures, change outputs,
and realign structure. We say more about both strategy issues and tools later. Regardless of
where one focuses, an effective job of operations consulting results in an alignment between
strategy and process dimensions that enhances the business performance of the client.
T h e M a n a ge m e nt Cons u lt in g In d u stry
The management consulting industry can be categorized in three ways: by size, by specialization, and by in-house and external consultants. Most consulting firms are small, generating
less than $1 million in annual revenue. Relative to specialization, although all large firms
provide a variety of services, they also may specialize by function, such as operations management, or by industry, such as manufacturing. Most large consulting companies are built on
information technology (IT) and accounting work. The third basis for segmentation, in-house
versus external, refers to whether a company maintains its own consulting organization or
buys consulting services from the outside. Internal consulting arms are common in large companies and are often affiliated with planning departments.
Consulting firms are also frequently characterized according to whether their primary skill
is in strategic planning or in tactical analysis and implementation. McKinsey & Company
and the Boston Consulting Group are standard examples of strategy-type companies, whereas
Gemini Consulting and A. T. Kearney focus rather extensively on tactical and implementation
projects. The big accounting firms and Accenture are known for providing a wide range of services. The major new players in the consulting business are the large information technology
firms such as Infosys Technology, Computer Sciences Corporation (CSC), Electronic Data
Systems (EDS), and IBM. Consultancies are faced with problems similar to those of their
clients: the need to provide a global presence, the need to computerize to coordinate activities,
and the need to continually recruit and train their workers. This has led consultancies to make
the hard choice of being very large or being a boutique firm. Being in the middle creates problems of lack of scale economies on the one hand and lack of focus and flexibility on the other.
The hierarchy of the typical consulting firm can be viewed as a pyramid. At the top of the
pyramid are the partners or seniors, whose primary function is sales and client relations. In
the middle are managers, who manage consulting projects or “engagements.” At the bottom
are juniors, who carry out the consulting work as part of a consulting team. There are gradations in rank within each of these categories (such as senior partners). The three categories are
frequently referred to colloquially as the finders (of new business), the minders (or managers) of the project teams, and the grinders (the consultants who do the work). Consulting
firms typically work in project teams, selected according to client needs and the preferences
of the project managers and the first-line consultants themselves. Getting oneself assigned to
interesting, high-visibility projects with good co-workers is an important career strategy of
most junior consultants. Being in demand for team membership and obtaining quality consulting experiences are critical for achieving long-term success with a consulting firm (or
being attractive to another firm within or outside consulting).
E c o n om ics of Cons ulting F irms
The economics of consulting firms have been written about extensively by David H. Maister. In
his classic article “Balancing the Professional Service Firm,” he draws the analogy of the consulting firm as a job shop, where the right kinds of “machines” (professional staff) must be correctly allocated to the right kinds of jobs (consulting projects). As in any job shop, the degree
of job customization and attendant complexity is critical. The most complex projects, which
Maister calls brain surgery projects, require innovation and creativity. Next come gray hair
projects, which require a great deal of experience but little in the way of innovation. A third
type of project is the procedures project, where the general nature of the problem is well known
and the activities necessary to complete it are similar to those performed on other projects.
Because consulting firms are typically partnerships, the goal is to maximize profits for
the partners. This, in turn, is achieved by leveraging the skills of the partners through the
effective use of midlevel and junior consultants. This is often presented as a ratio of partners to midlevel and junior consultants for the average project. (See Exhibit 25.1 for a
Finders
Partners or senior
consultants whose primary
function is sales and client
relations.
Minders
Managers of a consulting
firm whose primary
function is managing
consulting projects.
Grinders
Junior consultants whose
primary function is to do
the work.
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exhibit 25.1
The Economics of Guru Associates
Level
No.
Target
Utilization
Partner (senior)
4
75%
Middle
8
Junior
20
Target Billable
Hours @ 2,000
Hours per Person
per Year
Billing
Rate
Fees
6,000
$400
$2,400,000
(see calculations
below)
75%
12,000
$200
$2,400,000
$150,000
$1,200,000
90%
36,000
$100
$3,600,000
$ 64,000
$1,280,000
Totals
Salary per
Individual
$8,400,000
Fees
Salaries
Total
Salaries
$2,480,000
$8,400,000
(2,480,000)
Contributions
$5,920,000
Overhead*
$2,560,000
Partner profits
$3,360,000
Per partner
$ 840,000
*Assume overhead costs of $80,000 per professional.
numerical example of how profitability is calculated for a hypothetical consulting firm,
Guru Associates.) Because most consulting firms are engaged in multiple projects simultaneously, the percentage of billable employee hours assigned to all projects (target utilization) will be less than 100 percent. A practice that specializes in cutting-edge, high-client
risk (brain surgery) work must be staffed with a high partner-to-junior ratio because lowerlevel people will not be able to deliver the quality of services required. In contrast, practices
that deal with more procedural, low-risk work will be inefficient if they do not have a lower
ratio of partners to juniors because high-priced staff should not be doing low-value tasks.
The most common method for improving efficiency is the use of uniform approaches to
each aspect of a consulting job. Accenture, the company most famous for this approach, sends
its new consultants through a boot camp at its St. Charles, Illinois, training facility. At this
boot camp, it provides highly refined, standardized methods for such common operations
work as systems design, process reengineering, and continuous improvement, and for the
project management and reporting procedures by which such work is carried out. Of course,
other large consulting firms have their own training methods and step-by-step procedures for
selling, designing, and executing consulting projects.
W he n Op e ra tio n s Co n su lt in g Is Need ed
The following are some of the major strategic and tactical areas where companies typically
seek operations consulting. Looking first at manufacturing consulting areas (grouped under
what could be called the 5 Ps of production), we have
∙
∙
∙
∙
∙
Plant: Adding and locating new plants; expanding, contracting, or refocusing existing
facilities.
People: Quality improvement, setting/revising work standards, learning curve analysis.
Parts: Make or buy decisions, vendor selection decisions.
Processes: Technology evaluation, process improvement, reengineering.
Planning and control systems: Supply chain management, ERP, MRP, shop-floor control, warehousing, distribution.
Obviously, many of these issues are interrelated, calling for systemwide solutions. Examples of common themes reflecting this are developing manufacturing strategy; designing and
implementing JIT systems; implementing MRP or proprietary ERP software such as SAP;
and systems integration involving client–server technology. Typical questions addressed are:
Operations Consulting
Chapter 25
How can the client cut lead times? How can inventory be reduced? How can better control
be maintained over the shop floor? Among the hot areas of manufacturing strategy consulting are sustainability, outsourcing, supply chain management, and global manufacturing networks. At the tactical level, there is a huge market for consulting in e-operations, product
development, ISO 9000 quality certification, and design and implementation of decentralized
production control systems.
Turning to services, while consulting firms in manufacturing may have broad specialties
in process industries on the one hand and assembly or discrete product manufacture on the
other, service operations consulting typically has a strong industry or sector focus. A common
consulting portfolio of specialties in services (and areas of consulting need) would include the
following:
Financial services (staffing, automation, quality studies)
Health care (staffing, billing, office procedures, phone answering, layout)
Transportation (route scheduling and shipping logistics for goods haulers, reservation systems, and baggage handling for airlines)
Hospitality (reservations, staffing, cost containment, quality programs)
For both manufacturing and service industries, the current hot area for consultants, as well
as in-house teams, is Lean Six Sigma. The reason is companies have reached their limit on
how much can be done by downsizing and are thus focusing on rigorously measuring and perfecting various processes. Pharmaceutical companies, large retailers, and food companies are
examples of industries with heavy demand for consultants who specialize in such programs.
W h e n A r e O p e r a t i o n s C o n s u l t a n t s N e e d e d ? Companies typically seek
out operations consultants when they are faced with major investment decisions or when they
believe they are not getting maximum effectiveness from their productive capacity. As an
example of the first type of situation, consider the following:
A national pie restaurant chain retained consultants to determine if a major addition to its freezer storage capacity was needed at its pie-making plant. Its lease
had run out on a nearby freezer warehouse, so the firm had to make a decision
rather quickly. The pie plant manager wanted to spend $500,000 for a capacity
increase. After analysis of the demand for various types of pies, the distribution
system, and the contractual arrangement with the shipper, the consultant concluded that management could avoid all but a $30,000 investment in capacity if
they did the following: Run a mixed-model production schedule for pies according to a forecast for each of 10 kinds of pies (for example, 20 percent strawberry,
30 percent cherry, 30 percent apple, and 20 percent other pies each two-day pie
production cycle). To do this, more timely information about pie demand at each
of the chain restaurants had to be obtained. This in turn required that information
links for pie requirements go directly to the factory. Previously the distributor
bought the pies and resold them to the restaurants. Finally, the company renegotiated pickup times from the pie plant to enable just-in-time delivery at the
restaurants. The company was in a much stronger bargaining situation than it had
been five years previously, and the distributor was willing to make reasonable
adjustments.
The lesson from this is that few investment decisions in operations are all or nothing,
and good solutions can be obtained by simply applying standard OSCM concepts of production planning, forecasting, and scheduling. The solution recognized that the problem must be
viewed at a systemwide level to see how better planning and distribution could substitute for
brick-and-mortar capacity.
675
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Section 5
THE OPERATIONS CO NSULTING PROCESS
LO 25–2
Illustrate the operations
analysis tools used in the
consulting industry
The broad steps in the operations consulting process (see Exhibit 25.2) are roughly the same
as for any type of management consulting. The major differences exist in the nature of the
problem to be analyzed and the kinds of analytical methods to be employed. Like general
management consulting, operations consulting may focus on the strategic level or tactical
level, and the process itself generally requires extensive interviewing of employees, managers, and, frequently, customers. If there is one large difference, it is that operations consulting
leads to changes in physical or information processes whose results are measurable immediately. General management consulting usually calls for changes in attitudes and culture, which
take longer to yield measurable results. The roles in which consultants find themselves range
from an expert, to a pair of hands, to a collaborative or process consultant. Generally, the collaborative or process consultation role is most effective in operations management consulting
projects. Some consulting firms now provide the expert role online.
The steps in a typical operations consulting process are summarized in Exhibit 25.2. A
book by Ethan M. Rasiel on the McKinsey & Company approach offers some practical guidelines for conducting consulting projects:
∙
∙
∙
∙
∙
∙
∙
∙
Be careful what you promise in structuring an engagement. Underpromise and overdeliver is a good maxim.
Get the team mix right. You can’t just throw four random people at a problem and
expect them to solve it. Think about what sorts of skills and personalities work best for
the project at hand, and choose your teammates accordingly.
The 80–20 rule is a management truth. Eighty percent of sales come from 20 percent of
the sales force; 80 percent of your time is taken up with 20 percent of your job; and so on.
Don’t boil the ocean. Don’t try to analyze everything—be selective in what you investigate.
Use the elevator test. If you know your solution so well that you can explain it clearly
and precisely to your client in a 30-second elevator ride, you are doing well enough to
sell it to the client.
Pluck the low-hanging fruit. If you can make an immediate improvement even though you
are in the middle of a project, do it. It boosts morale and gives credibility to your analysis.
Make a chart every day. Commit your learning to paper; it will help push your thinking
and assure that you won’t forget it.
Hit singles. You can’t do everything, so don’t try. It’s better to get to first base consistently than to try to hit a home run and strike out 9 times out of 10.
exhibit 25.2
Stages in the Operations Consulting Process
8. Assemble
learnings
from the
study
1. Sales and
proposal
development
7. Assure client
satisfaction
2. Analyze
problem
Client
Success
6. Implement
changes
(as agreed upon)
5. Present
final
report
3. Design,
develop,
and test
alternative
solutions
4. Develop
systematic
performance
measures
Operations Consulting
∙
∙
∙
∙
Chapter 25
Don’t accept “I have no idea.” Clients and their staff always know something, so probe
them for some educated guesses.
Engage the client in the process. If the client doesn’t support you, the project will stall.
Keep your clients engaged by keeping them involved.
Get buy-in throughout the organization. If your solution is to have lasting impact on
your client, you have to get support for it throughout the organization.
Be rigorous about implementation. Making change happen takes a lot of work. Be
­rigorous and thorough. Make sure someone takes responsibility for getting the job done.
Op e r a t ions Cons ulting To o l Kit
Operations consulting tools can be categorized as tools for problem definition, data gathering, data analysis and solution development, cost impact and payoff analysis, and
implementation. These—along with some tools from strategic management, marketing, and information systems that are commonly used in OSCM consulting—are noted in
Exhibit 25.3 and are described next. Note that several of these tools are used in more than
one stage of a project.
P r ob le m D e finition Tools
I s s u e T r e e s Issue trees are used by McKinsey to structure or map the key problems
to be investigated and provide a working initial hypothesis as to the likely solution to these
problems. As can be seen in Exhibit 25.4, a tree starts with the general problem (increase
exhibit 25.3
Operations Consulting Tool Kit
Problem Definition
Issue trees
Customer surveys
Gap analysis
Employee surveys
Five forces model
Data Gathering
Plant tours/audits
Work sampling
Flowcharts
Organization charts
Data Analysis and
Solution Development
Problem analysis
(SPC tools)
Bottleneck analysis
Computer simulation
Statistical tools
Cost Impact and
Payoff Analysis
Decision trees
Balanced scorecard
Stakeholder analysis
Implementation
Responsibility charts
Project management techniques
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Special Topics
exhibit 25.4
Issue Tree for Acme Widgets
Sales force
organization
Change
sales
strategy
Sales force
skill base
Promotion
strategy
Product quality
Increase
widget
sales
Improve
marketing
strategy
Packaging
Consumer
advertising
strategy
Raw materials
sourcing
Reduce
unit cost
Production process
Distribution system
E. M. Rasiel, The McKinsey Way: Using the Techniques of the World’s Top Strategic Consultants to Help You and Your
Business, (New York, McGraw-Hill, 1998), p. 12. Used with permission.
widget sales) and then goes level by level until potential sources of the problem are identified.
Once the tree is laid out, the relationships it proposes and possible solutions are debated, and
the project plan is then specified.
C u s t o m e r S u r v e y s Frequently, OSCM consultants are called in to address problems
identified by customer surveys performed by marketing consultants or marketing staff.
Often, however, these are out of date or are in a form that does not separate process issues
from advertising or other marketing concerns. Even if the surveys are in good form, calling
customers and soliciting their experience with the company is a good way to get a feel for
process performance. A key use of customer surveys is customer loyalty analysis, although
in reality customers are not so much “loyal” (your dog, Spot, is loyal) as “earned” through
effective performance. Nevertheless, the term loyalty captures the flavor of how well an
organization is performing according to three critical market measures: customer retention,
share of wallet, and price sensitivity relative to competitors. Having such information available
helps the OSCM consultant drill down into the organization to find what operational factors
are directly linked to customer retention. Although loyalty studies are usually performed by
marketing groups, OSCM consultants should be aware of their importance.
G a p A n a l y s i s Gap analysis is used to assess the client’s performance relative to the
expectations of its customers, or relative to the performance of its competitors. An example is
shown in Exhibit 25.5.
Operations Consulting
ex hibit 25.5
Chapter 25
Issue Tree for Acme Widgets
Actual versus Desired Performance
Critical Success Factors
1
2
3
4
5
6
7
8
9
10
Service level
Quality
Gap
Customization
Availability
Response time
One-call resolution
Actual
Desired
Source: Deloitte & Touche Consulting Group
Another form of gap analysis is benchmarking particular client company processes against
exemplars in the process and measuring the differences. For example, if one is interested in
billing process accuracy and problem resolution, American Express would be the benchmark;
for timeliness and efficiency in railway transportation, Japanese Railways; for order entry in
catalog sales, it would be L.L.Bean.
E m p l o y e e S u r v e y s Such surveys range from employee satisfaction surveys
to suggestion surveys. A key point to remember is if the consultant requests employee
suggestions, such information must be carefully evaluated and acted upon by management. A
few years ago, Singapore Airlines distributed a questionnaire to its flight personnel, but made
the mistake of not following through to address their concerns. As a result, the employees
were more critical of the company than if the survey had not been taken, and to this day the
company does not use this form of evaluation.
T h e F i v e F o r c e s M o d e l This is one of the better-known approaches to evaluating
a company’s competitive position in light of the structure of its industry. The five forces
are buyer power, potential entrants, raw material suppliers, substitute products, and industry
rivals. The consultant applies the model by developing a list of factors that fit under each of
these headings. Some examples of where a client’s competitive position might be strong are
when buyers have limited information, there are major barriers to potential entrants, there are
many alternative suppliers, there are few substitute products (or services), or there are few
industry rivals.
Often used with the five forces model is the value chain, such as shown in Exhibit 25.6.
The value chain provides a structure to capture the linkage of organizational activities that
create value for the customer and profit for the firm. It is particularly useful to get across the
notion that operations and the other activities must work cross-functionally for optimal organizational performance (and avoid the dreaded “functional silo” syndrome).
A tool similar to the five forces model is SWOT analysis. This is a somewhat more general method of evaluating an organization and has the advantage of being easy to remember:
Strengths of the client, Weaknesses of the client, Opportunities for the client in the industry,
and Threats from competitors or the economic and market environment.
D at a G a the r ing
P l a n t T o u r s / A u d i t s These can be classified as manufacturing tours/audits and
service facility tours/audits. Full manufacturing audits are a major undertaking, entailing
measurement of all aspects of the production facility and processes, as well as support
activities such as maintenance and inventory stockkeeping. Frequently these require several
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exhibit 25.6
Value Chain
Firm infrastructure
gi
Mar
Human resource management
Support
activities
n
Technology development
Inbound
logistics
Operations
Upstream value activities
Outbound
logistics
Marketing
and sales
Service
Mar
gin
Procurement
Downstream value activities
Based on Harvard Business School Press. From M. E. Porter, Competition in Global Industries, (Boston,MA, 1986), p. 24.
weeks, utilizing checklists developed explicitly for the client’s industry. Plant tours, on the
other hand, are usually much less detailed and can be done in a half day. The purpose of
the tour is to get a general understanding of the manufacturing process before focusing on a
particular problem area. To collect consistent information, the members of the study team in
a tour use the same generic checklist or general questions.
The quick plant assessment (QPA) tour is designed to enable a study team to determine
the “leanness” of a plant in just 45 minutes. The approach uses a 20-item questionnaire and
an 9-category item rating sheet (see “Quick Plant Assessment” Exercise at the end of the
­chapter). During the tour, team members talk with workers and managers and look for evidence of best practices. At the end of the tour, members discuss their impressions and fill
out the worksheets. The categories are key to the tour. Their features are summarized in the
nearby OSCM at Work box, “Quick Plant Assessment.”
Complete service facility audits are also a major undertaking, but they differ from manufacturing audits in that, when properly done, they focus on the customer’s experience as much
as on the utilization of resources. Typical questions in a service audit address time to get service, the cleanliness of the facility, staff sizing, and customer satisfaction. A service facility
tour or walk-through can often be done as a mystery shopper, where the consultant actually
partakes of the service and records his or her experiences.
OSCM AT WORK
Quick Plant Assessment
1.
Customer focus. A customer-oriented workforce will
take pride in satisfying both external and internal customers. The extent of this orientation should be apparent even in a brief plant tour. For example, when asked
about the next step in the process, customer-aware
employees will respond by giving a person’s name
or product, rather than saying that they just put it on
the pallet and it’s moved later. Cordiality to the touring
group and posted quality and customer satisfaction
jac66107_ch25_671-690.indd 680
ratings are other signs of a customer-oriented workforce. (Questions 1, 2, and 20 on the QPA questionnaire
relate to this measure. This questionnaire is included at
the end of this chapter.)
2.
Safety, cleanliness, and order. The physical environment of a plant is important to operating effectiveness. Cleanliness, low noise levels, good lighting, and
air quality are obvious things to look for. Labeling and
tracking of all inventory items, not just expensive ones,
should be in evidence. (Not having the required nuts
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Operations Consulting
3.
4.
5.
6.
and bolts can be as disruptive to production as lacking
a major component.) (Questions 3–5 and 20)
Visual management/Scheduling. Production management tools such as work instructions, kanban schedules, and quality and productivity charts should be
easily visible. Posted workflow diagrams linking each
stage of a process are particularly effective visual cues.
In addition, scheduling typically involves some mechanism for pacing of the workflow based on demand.
(Questions 2, 4, 6–10, 11, and 20)
Use of space, movement efficiency, and product line
flow. Good indicators of efficient space utilization are
minimum material movement over short distances, use
of efficient containers; materials stored at the point of
use, not in separate inventory storage areas; tooling
kept near the machines; and product flow layout rather
than process layout. (Questions 7, 12, 13, and 20)
Teamwork. Discussions with workers and visible indicators of teamwork such as names of teams over a work
area and productivity award banners are quick ways of
determining how the workforce feels about their jobs,
the company, and their co-workers. (Questions 9, 14, 15,
and 20)
Maintenance of equipment. Purchase dates and
equipment costs should be stenciled on the side of
machinery, and maintenance records should be posted
nearby. Asking people on the factory floor how things
are working and whether they are involved in purchasing tools and equipment is also indicative of the extent
to which workers are encouraged to address these
issues. (Questions 16 and 20)
7.
8.
9.
681
Chapter 25
Management of complexity and variability. This
depends greatly on the type of industry. Obviously,
industries with narrow product lines have less difficulty handling complexity and variability. Indicators to
watch for in general are the number of people manually
recording data and the number of keyboards available
for data entry. (Questions 8, 17, and 20)
Supply chain integration. It is generally desirable to
work closely with a relatively small number of dedicated and supportive suppliers. A rough estimate of
the number of suppliers can be ascertained by looking
at container labels to see what supplier names appear
on containers. Containers that appear to be designed
and labeled specifically for customized parts shipped
to a plant indicate the extent to which a strong supplier
partnership exists. A sign of poor supply chain integration is lots of paperwork on the receiving dock. This
indicates lack of a smooth pull system where plants
pull the materials from their suppliers as if it was just
another link in the pull system for each product line.
(Questions 18 and 20)
Quality commitment. Attention to quality is evidenced
in many ways, including posting of quality awards, quality scorecards, and quality goal statements. Quality is
reflected in many of the other plant activities such as
product development and startups. (Questions 8, 9, 15,
17, 19, and 20)
Modified from R. Eugene Goodson, “Read a Plant—Fast,” Harvard
Business Review 80, no. 5 (May 2002), pp. 105–13.
Manufacturing
professionals take a
tour of the Lincoln
Electric Machine
Division of the
Cleveland headquarters
and factory, where
they see the Lincoln
manufacturing plan
in action on the plant
floor. The tours
highlight five different
locations on the
manufacturing floor
where more than 300
welding machine models
and 1,600 accessories
are made each day.
Courtesy of The Lincoln
Electric Company
jac66107_ch25_671-690.indd
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01/10/17 12:04 PM
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Section 5
Special Topics
W o r k S a m p l i n g Work sampling entails random sampling observations of work
activities, designed to give a statistically valid picture of how time is spent by a worker or the
utilization of equipment. Diary studies are another way to collect activity data. These are used
by consultants to get an understanding of specific tasks being performed by the workforce.
In these, the employee simply writes down the activities he or she performs during the week
as they occur. This avoids the problem of having analysts look over a worker’s shoulder to
gather data. Examples of where these studies are used include library front desks, nursing,
and knowledge work.
F l o w c h a r t s Flowcharts can be used in both manufacturing and services to track
materials, information, and people flows. Workflow software such as Optima! and BPR
Capture are widely used for process analysis. In addition to providing capabilities for defining
a process, most workflow software provides four other basic functions: work assignment
and routing, scheduling, work list management, and automatic status and process metrics.
Flowcharts used in services—service blueprints—are basically the same thing, but add the
important distinction of the line of visibility to clearly differentiate activities that take place
with the customer versus those that are behind the scenes. In our opinion, the service blueprint
is not used to its full potential by consulting firms, perhaps because relatively few consultants
are exposed to them in their training.
O r g a n i z a t i o n C h a r t s Organization charts are often subject to change, so care must
be taken to see who really reports to whom. Some companies are loath to share organization
charts externally. Several years ago, a senior manager from a large electronics firm told us that
a detailed organization chart gives free information to the competition.
D a ta A n a lysis an d So lu tio n Develo p men t
P r o b l e m A n a l y s i s ( S P C T o o l s ) Pareto analysis, fishbone diagrams, run charts,
scatter diagrams, and control charts are fundamental tools in virtually every continuous
improvement project. Pareto analysis is applied to inventory management under the heading
of ABC analysis. Such ABC analysis is still the standard starting point of production control
consultants when examining inventory management problems. Fishbone diagrams (or causeand-effect diagrams) are a great way to organize one’s first cut at a consulting problem (and
they make a great impression when used to analyze, for example, a case study as part of
the employment selection process for a consulting firm). Run charts, scatter diagrams, and
control charts are tools that one is simply expected to know when doing operations consulting.
B o t t l e n e c k A n a l y s i s Resource bottlenecks appear in most OSCM consulting
projects. In such cases, the consultant has to specify how available capacity is related to
required capacity for some product or service in order to identify and eliminate the bottleneck.
This isn’t always evident, and abstracting the relationships calls for the same kind of logical
analysis used in the classic “word problems” you loved in high school algebra.
C o m p u t e r S i m u l a t i o n Computer simulation analysis has become a very common
tool in OSCM consulting. The most common general-purpose simulation packages are
Extend and Crystal Ball. SimFactory and ProModel (for manufacturing systems), MedModel
(hospital simulation), and Service Model are examples of specialized packages. For smaller
and less complex simulation, consultants often use Excel. Chapter 10 introduces the topic of
simulation in this book.
A growing interest in simulation is in the analysis of “system dynamics.” System dynamics is a language that helps us see the patterns that underlie complex situations. These complex situations are modeled using causal loop diagrams that are useful when factors either
enhance or degrade system performance. Causal loops are of two types: reinforcing loops and
balancing loops. Reinforcing loops are positive feedback loops driving positive values in criteria important to the system. Balancing loops reflect the mechanisms that counter reinforcing
loops, thereby driving the system toward equilibrium. By way of example, with reference to
Operations Consulting
ex hibit 25.7
Chapter 25
Causal Loop Analysis
Quality
goal
Effective
time
required
Quality
standard
B
Time
pressure
R
Actual
quality
R - Reinforcing loop
B - Balancing loop
Exhibit 25.7, suppose you have a quality goal that is reflected in a quality standard. The reinforcing loop (R) indicates that the standard, if left unmodified, would yield an ever-increasing
(or decreasing) level of actual quality. In reality, what happens is that the balancing loop (B)
comes into play. Effective time required to meet the standard determines time pressure (on the
workers), which, in turn, modifies the actual quality achieved and ultimately achievement of
the quality standard itself. An obvious use of the system shown here would be to hypothesize
the consequences of raising the quality goal, or raising or lowering the values of the other
variables in the system. In addition to its use in problem analysis, causal loop analysis simulations are often used by consultants to help client companies become more effective learning
organizations.
S t a t i s t i c a l T o o l s Correlation analysis and regression analysis are expected skills for
consulting in OSCM. The good news is that these types of analyses are easily performed with
spreadsheets. Hypothesis testing is mentioned frequently in the consulting firm methodology
manuals, and one should certainly be able to perform Chi-square and t-tests in analyzing data.
Two other widely used tools that use statistical analysis are queuing theory and forecasting.
Consultants frequently use queuing theory to investigate how many service channels are
needed to handle customers in person or on the phone. Forecasting problems likewise arise
continually in OSCM consulting (such as forecasting the incoming calls to a call center).
A newly emerging tool (not shown on our exhibit) is data envelopment analysis. DEA
is a linear programming technique used to measure the relative performance of branches of
multisite service organizations such as banks, franchise outlets, and public agencies. A DEA
model compares each branch with all other branches and computes an efficiency rating based
on the ratio of resource inputs to product or service outputs. The key feature of the approach
is that it permits using multiple inputs such as materials and labor hours, and multiple outputs
such as products sold and repeat customers, to get an efficiency ratio. This feature provides a
more comprehensive and reliable measure of efficiency than a set of operating ratios or profit
measures.
C o s t I m pa ct a nd Pa yoff A n a lysis
D e c i s i o n T r e e s Decision trees represent a fundamental tool from the broad area of
risk analysis. They are widely used in examining plant and equipment investments and R&D
projects. Decision trees are built into various software packages such as TreeAge (www.
treeage.com).
S t a k e h o l d e r A n a l y s i s Most consulting projects impact in some way each of five
types of stakeholders: customers, stockholders, employees, suppliers, and the community.
The importance of considering the interest of all stakeholders is reflected in the mission
statements of virtually all major corporations and, as such, provides guidance for consultants
in formulating their recommendations.
683
684
Special Topics
Section 5
exhibit 25.8
Dashboard for Suppliers
Motion
Source
E-Link
Accessories
30
40
50 60
Motion
Source
E-Link
70
20
80
Accessories
90
10
100
110
0
Delivery Days
[SupplierType]
30
20
Sights
10
40
50 60 70
Motion
Source
E-Link
80
90
110
120
0
Accessories
100
Sights
150
100
200
250
50
0
Delivered Qty (×100,000)
[SupplierType]
Sights
300
350
Damaged Qty (×10)
[SupplierType]
B a l a n c e d S c o r e c a r d In an attempt to reflect the particular needs of each stakeholder
group in a performance measurement system, accountants have developed what is termed a
balanced scorecard. (Balanced refers to the fact that the scorecard looks at more than just
the bottom line or one or two other performance measures.) The Bank of Montreal has used
the balanced scorecard notion in setting specific goals and measures for customer service,
employee relations, return to owners, and community relations. A key feature of the system is
that it is tailored to what senior management and branch-level management can control.
P r o c e s s D a s h b o a r d s In contrast to the balanced scorecard, which focuses on
organizationwide performance data, process dashboards are designed to provide summary
performance updates for specific processes. Dashboards consist of a selection of performance
metrics presented in graphical form with color-coding of trend lines, alarms in the form of
exclamation marks, and so forth, to show when key indicators are nearing a problem level. For
example, three different dials on a dashboard for suppliers are shown in Exhibit 25.8.
Im ple m en t a tio n
R e s p o n s i b i l i t y C h a r t s A responsibility chart is used in planning the task
responsibilities for a project. It usually takes the form of a matrix with tasks listed across the
top and project team members down the side. The goal is to make sure that a checkmark exists
in each cell to assure that a person is assigned to each task.
P r o j e c t M a n a g e m e n t T e c h n i q u e s Consulting firms use the project
management techniques of CPM/PERT and Gantt charts to plan and monitor the entire
portfolio of consulting engagements of the firm, as well as individual consulting projects.
Microsoft Project and Primavera Project Planner are examples of commonly used software to
automate such tools. Evolve Software has developed a software suite for professional service
firms, modeled on ERP for manufacturing, that allows management to integrate opportunity
management (the selling process), resource management, and delivery management. It should
be emphasized that these planning tools are very much secondary to the people management
skills needed to successfully execute a consulting project. This admonition is likewise true for
all of the tools we have discussed in this section.
BUSI NESS PROCESS REENGINEERING (BPR)
LO 25–3
Analyze processes
using business process
reengineering concepts.
Business process reengineering is the radically restructuring of business processes to significantly improve customer service, reduce cost, and become competitive. It uses many of the
tools just discussed to achieve these goals.
The concept of reengineering has been around for nearly two decades and was implemented in a piecemeal fashion in organizations. Production organizations have been in the
vanguard without knowing it. They have undertaken reengineering by implementing concurrent engineering, lean production, cellular manufacturing, group technology, and pull-type
production systems. These represent a fundamental rethinking of the manufacturing process.
Operations Consulting
Chapter 25
Reengineering is often compared to total quality management (TQM), a topic covered
in Chapter 12. Some people have said that the two are, in fact, the same, whereas others
have even argued that they are incompatible. Both concepts are centered on a customer
focus. The concepts of teamwork, worker participation and empowerment, cross-functionality, process analysis and measurement, supplier involvement, and benchmarking are significant contributions from quality management. In addition, the need for a “total” view
of the organization has been reemphasized by quality management in an era of extensive
functionalization of business. Quality management has also influenced company culture
and values by exposing organizations to the need for change. The basic difference between
the two is that quality management has emphasized continuous and incremental improvement of processes that are in control, whereas reengineering is about radical, discontinuous change through process innovation. Thus, a given process is enhanced by TQM until
its useful lifetime is over, at which point it is reengineered. Then, enhancement is resumed
and the entire cycle starts again. As business circumstances change in major ways, so must
process designs.
P r i n cip le s of Re e ngine e rin g
Reengineering is about achieving a significant improvement in processes so that contemporary customer requirements of quality, speed, innovation, customization, and service are met.
The following are seven principles or rules for reengineering and integration that can be used
to guide a process reengineering project.
R u l e 1 . O r g a n i z e a r o u n d O u t c o m e s , N o t T a s k s Several specialized tasks
previously performed by different people should be combined into a single job. This could be
performed by an individual “case worker” or by a “case team.” The new job created should
involve all the steps in a process that creates a well-defined outcome. Organizing around
outcomes eliminates the need for handoffs, resulting in greater speed, productivity, and customer
responsiveness. It also provides a single knowledgeable point of contact for the customer.
Rule 2. Have Those Who Use the Output of the Process Perform
t h e P r o c e s s In other words, work should be carried out where it makes the most sense
to do it. This results in people closest to the process actually performing the work, which shifts
work across traditional intra- and interorganizational boundaries. For instance, employees
can make some of their own purchases without going through purchasing, customers can
perform simple repairs themselves, and suppliers can be asked to manage parts inventories.
Relocating work in this fashion eliminates the need to coordinate the performers and users
of a process.
Rule 3. Merge Information-Processing Work into the Real
W o r k t h a t P r o d u c e s t h e I n f o r m a t i o n This means that people who
collect information should also be responsible for processing it. It minimizes the need
for another group to reconcile and process that information, and greatly reduces errors by
cutting the number of external contact points for a process. A typical accounts payable
department that reconciles purchase orders, receiving notices, and supplier invoices is a
case in point. By eliminating the need for invoices by processing orders and receiving
information online, much of the work done in the traditional accounts payable function
becomes unnecessary.
Rule 4. Treat Geographically Dispersed Resources as Though
T h e y W e r e C e n t r a l i z e d Information technology now makes the concept of hybrid
centralized/decentralized operations a reality. It facilitates the parallel processing of work
by separate organizational units that perform the same job, while improving the company’s
overall control. For instance, centralized databases and telecommunication networks now
allow companies to link with separate units or individual field personnel, providing them with
economies of scale while maintaining their individual flexibility and responsiveness to customers.
685
Reengineering
The radically resturcturing
of business processes
to significantly improve
customer service, reduce
cost, and become
competitive.
686
Special Topics
Section 5
Rule 5. Link Parallel Activities Instead of Integrating Their
R e s u l t s The concept of integrating only the outcomes of parallel activities that must
eventually come together is the primary cause for rework, high costs, and delays in the final
outcome of the overall process. Such parallel activities should be linked continually and
coordinated during the process.
Rule 6. Put the Decision Point Where the Work Is Performed,
a n d B u i l d C o n t r o l i n t o t h e P r o c e s s Decision making should be made part
of the work performed. This is possible today with a more educated and knowledgeable
workforce plus decision-aiding technology. Controls are now made part of the process. The
vertical compression that results produces flatter, more responsive organizations.
R u l e 7 . C a p t u r e I n f o r m a t i o n O n c e — a t t h e S o u r c e Information should
be collected and captured in the company’s online information system only once—at the
source where it was created. This approach avoids erroneous data entries and costly reentries.
G uide line s f o r Imp lemen tatio n
The principles of business process reengineering just enumerated are based on a common
platform of the innovative use of information technology. But creating a new process and sustaining the improvement requires more than a creative application of information technology.
A detailed study of reengineering applications in 765 hospitals yielded the following three
managerial guidelines that apply to almost every organization contemplating reengineering:
1.
Codification of reengineering. Organizationwide change programs such as reengineering are complex processes whose implementation may be separated by space and
time. Middle managers are often left to implement significant portions of reengineering proposals. Codifying provides guidance and direction for consistent, efficient
implementation.
2. Clear goals and consistent feedback. Goals and expectations must be clearly established, preapplication baseline data gathered, and the results monitored and fed back
to employees. Without clear feedback, employees often became dissatisfied and their
perceptions of reengineering success can be quite different from actual outcomes.
For example, the hospital researchers
found that, at 10 hospitals they studied in depth, most employees in 4 of
them felt that the reengineering program had done little to change costs,
even though their costs had actually
dropped 2 to 12 percent relative
to their competitors’. On the other
hand, 4 hospitals in which most felt
that reengineering had lowered costs
actually experienced an increase in
relative costs and a deterioration of
their cost position.
3. High executive involvement in
process changes. A high level of
involvement by the chief executive
officer in major process changes
(procedure changes in hospitals,
for example) improves reengineering outcomes. Changes that require
The British retailer Marks & Spencer has gone through company
reductions of managers and employreengineering, producing Plan A, a 100-point eco-plan. It is reducing how
ees are certainly less popular and
much of its clothing and packaging ends up as landfill by improving
more difficult. It is better that these
packaging, recycling more, and using fewer plastic bags.
© Chris Ratcliffe/Bloomberg via Getty Images
be done using a more long-term plan.
Operations Consulting
Chapter 25
687
Concept Connections
LO 25–1 Explain operations consulting and how money is made in the industry.
Summary
∙ Consulting firms specializing in operations and supply chain management focus on improving a firm’s
competitiveness by improving processes.
∙ These firms can bring expertise that the client firm
does not have. The consultant can do specialized analysis, such as simulation and optimization.
∙ A consulting firm makes money by charging for services, typically based on a set of rates that depend on
the relative experience of the consultant. The most
experienced consultants run the projects and are billed
at the highest rates. Partners share the profits of the
consulting practice.
Key Terms
Operations consulting Assisting clients in develop-
ing operations strategies and improving production
processes.
Finders Partners or senior consultants whose primary
function is sales and client relations.
Minders Managers of a consulting firm whose primary
function is managing consulting projects.
Grinders Junior consultants whose primary function is
to do the work.
LO 25–2 Illustrate the operations analysis tools used in the consulting industry.
Summary
∙ The consulting firm uses tools to aid in understanding
problems, collecting data, developing solutions, analyzing the payoff from proposed changes, and implementing recommendations.
∙ These tools provide structure to the consulting practice and are matched to the needs of the client. Many
of these tools have already been discussed in earlier
chapters of this book.
LO 25–3 Analyze processes using business process reengineering concepts.
Summary
∙ Compared to the approach normally taken to improve
a process, reengineering is different. Here the idea is
to radically rethink how business processes are done
with the goal of achieving a dramatic improvement in
performance.
Key Terms
Reengineering The radically resturcturing of business
processes to significantly improve customer service,
reduce cost, and become competitive.
Discussion Questions
LO 25–1
1. Check the Websites of the consulting companies listed in the chapter. Which ones
impressed you most as a potential client and as a potential employee?
Boston Consulting Group (www.bcg.com)
Deloitte Touche Tohmatsu (www.deloitte.com)
McKinsey & Co. (www.McKinsey.com)
2. What does it take to be a good consultant? Is this the career for you?
688
Special Topics
Section 5
LO25–2
LO25–3
3. In discussing characteristics of efficient plants, Goodson, developer of rapid plant assessments (see the OSCM at Work box), suggests that numerous forklifts are a sign of poor
space utilization. What do you think is behind this observation?
4. Think about the registration process at your university. Develop a flowchart to understand
it. How would you radically redesign this process?
5. Have you driven a car lately? Try not to think of the insurance claim settlement process
while you drive! How would you reengineer your insurance company’s claim process?
Objective Questions
LO25–1
LO25–2
LO25–3
1. In what three ways can market leadership be obtained?
2. The process of running a consulting firm is analogous to what type of manufacturing
process structure?
3. What are the 5 Ps of production in which firms typically seek operations consulting?
4. What is the current “hot area” for operations consultants in both manufacturing and services?
5. What methodology is used to assess a client’s performance relative to the expectations of
its customers or the performance of its competitors?
6. What type of plant tour is designed to determine the “leanness” of a plant in just 30 minutes?
7. What tool is used to reflect the particular needs of each stakeholder group in a performance measurement system? (Answer in Appendix D)
8. What tool is used to ensure that all tasks in a project have the right mix of project team
members assigned?
9. An equipment manufacturer has the following steps in its order entry process:
a. Take the order and fax it to order entry.
b. Enter the order into the system (10 percent unclear or incorrect).
c. Check stock availability (stock not available for 15 percent of orders).
d. Check customer credit (10 percent of orders have credit questions).
e. Send bill of materials to warehouse.
The order receipt to warehouse cycle time is typically 48 hours; 80 percent of the orders
are handled without error; and order-handling costs are 6 percent of order revenue. Should
you reengineer this process or is continuous improvement the appropriate approach? If
you choose to reengineer, how would you go about it?
10. Is the business reengineering process more gradual, more radical, or about the same as
the TQM process?
11. What concept provides guidance and direction for consistent, efficient implementation of
BPR projects? (Answer in Appendix D)
Exercise: Quick Plant Assessment
This exercise is designed to support a plant tour event
conducted as part of a class.
This questionnaire is focused on assessing the “leanness” of a manufacturing plant. It might be useful to review
the material on “lean” processes in Chapter 14 where the
concepts considered in the questionnaire are described.
The questionnaire can be modified for non-manufacturing type processes, for example services or warehouses, depending on the facility that is being visited.
We would suggest working with a team of two to
four people and taking at least a 45-minute tour of a plant.
It would be most useful if your tour guide were knowledgeable about the operation of the plant and willing to
answer questions. At the conclusion of the tour, rate what
you observed using the Quick Plant Assessment (QPA)
questionnaire and Score Sheet.
In class, discuss those areas where leanness is generally lacking across the plant(s) visited.
Additional analysis for a consulting report:
1. Use the results from filling out the QPA Questionnaire in Exhibit 25.9 and your team’s observations
to develop a consensus score for each Assessment
Category in the QPA Score Sheet.
2. Prioritize targets of opportunity for management.
3. Develop a two-page action plan that you would
present to management to help them make
improvements.
Operations Consulting
ex hibit 25.9
689
Chapter 25
Quick Plant Assessment Questionnaire
Yes
No
1. A
re visitors welcome to the plant and given information about how the plant operates, the workforce, customers, and products?
2. Are ratings for product quality and customer satisfaction displayed for the workforce and customers to view?
3. Is the plant clean, orderly, and well lit? Is the air quality good, and are noise levels low?
4. Is a visual labeling system used to identify inventory locations, storage places for tools, process areas, and
movement lanes?
5. Does it appear that everything has a specific place, and everything is stored in its place?
6. Are performance measures and goals for these measures prominently posted and up to date?
7. A
re production materials brought to and stored near where they are used rather than in separate remote
storage areas?
8. Are specific instructions for how work is to be done and quality specifications visible at all workstations?
9. Are up to date charts that show productivity, quality, and safety visible in all process areas?
10. Is each process area scheduled using some type of pacing mechanism so workers can see real-time status
against the schedule?
11. C
an the current state of the plant be viewed from a central control room, on a status board, or online
computer display?
12. Is material moved only once and as short a distance as possible? Is material moved efficiently in appropriate containers?
13. Is the plant laid out in continuous product line flows rather than in “shops”?
14. A
re workers organized in teams and are they trained and empowered to engage in problem solving and
ongoing improvements?
15. Do employees seem committed to continuously improving processes?
16. Is there a formal plan for equipment preventive maintenance and improvement of tools and processes?
17. Is there a process for managing projects (especially new product start-ups), with cost and timing goals?
18. Is there a supplier certification process with measures for delivery, cost, and quality performance? Are these
measures shared with suppliers frequently?
19. Are fail-safe methods used in the processes to prevent common product quality problems?
20. Would you buy the products this plant produces?
ex hibit 25.10
QPA Score Sheet
Assessment category
Relevant
Questions
Customer focus
1, 2, 20
Safety, cleanliness, and order
3, 4, 5, 20
Visual management/Scheduling
2, 4, 6, 7, 8, 9, 10, 11, 20
Use of space, movement efficiency, and product
line flow
7, 12, 13, 20
Teamwork
9, 14, 15, 20
Maintenance of equipment
16, 20
Management of complexity and variability
8, 17, 20
Supply chain integration
18, 20
Quality commitment
8, 9, 15, 17, 19, 20
Number
of Yes’s
Ratio of Yes’s to
Number of Relevant
Questions
690
Section 5
Special Topics
Practice Exam
In each of the following, name the term defined or answer
the question. Answers are listed at the bottom.
1. Name the three categories of consultants.
2. This type of project requires a great deal of experience but little innovation.
3. Accenture is well known for this type of approach to
training consultants.
4. Target utilization is usually highest for which level of
consultant?
5. McKinsey uses these to structure or map the key
problems to be investigated.
6. These are the five forces of the five forces model.
7. Gap analysis measures the difference between these
two factors.
8. Rapid plant assessment is used to measure this
variable.
9. An accounting approach to reflect the needs of each
stakeholder is called this.
10. In contrast to TQM, this approach seeks radical
change through innovation.
Answers to Practice Exam 1. Finders, minders, and grinders 2. Gray hair 3. Uniform approaches 4. Junior level 5. Issue trees 6. Buyer power,
potential entrants, suppliers, substitute products, and industry rivals 7. Actual and desired performance 8. Leanness of a plant 9. Balanced scorecard
10. Business process reengineering
A PPENDIX A
LINEAR PROGRAMMING USING THE
E X C E L S O LV E R
The key to profitable operations is making the best use of available resources of people, material, plant and equipment, and money. Today’s manager has a powerful mathematical modeling tool available for this purpose with linear programming. In this appendix, we will show
how the use of the Microsoft Excel Solver to solve LP problems opens a whole new world to
the innovative manager and provides an invaluable addition to the technical skill set for those
who seek careers in consulting. In this appendix, we use a product-planning problem to introduce this tool. Here we find the optimal mix of products that have different costs and resource
requirements. This problem is certainly relevant to today’s competitive market. Extremely
successful companies provide a mix of products, from standard to high-end luxury models.
All these products compete for the use of limited production and other capacity. Maintaining
the proper mix of these products over time can significantly bolster earnings and the return
on a firm’s assets.
We begin with a quick introduction to linear programming and conditions under which the
technique is applicable. Then, we solve a simple product-mix problem. Other linear programming applications appear throughout the rest of the book.
Linear programming (or simply LP) refers to several related mathematical techniques
used to allocate limited resources among competing demands in an optimal way. LP is the
most widely used of the approaches falling under the general heading of mathematical optimization techniques and has been applied to many operations management problems. The
following are typical applications:
Aggregate sales and operations planning: Finding the minimum-cost production schedule.
The problem is to develop a three- to six-month plan for meeting expected demand given
constraints on expected production capacity and workforce size. Relevant costs considered
in the problem include regular and overtime labor rates, hiring and firing, subcontracting,
and inventory carrying cost.
Service/manufacturing productivity analysis: Comparing how efficiently different service
and manufacturing outlets are using their resources compared to the best-performing unit.
This is done using an approach called data envelopment analysis.
Product planning: Finding the optimal product mix where several products have different
costs and resource requirements. Examples include finding the optimal blend of chemicals
for gasoline, paints, human diets, and animal feeds. Examples of this problem are covered
in this chapter.
Product routing: Finding the optimal way to produce a product that must be processed
sequentially through several machine centers, with each machine in the center having its
own cost and output characteristics.
Vehicle/crew scheduling: Finding the optimal way to use resources such as aircraft, buses,
or trucks and their operating crews to provide transportation services to customers and
materials to be moved between different locations.
Process control: Minimizing the amount of scrap material generated by cutting steel,
leather, or fabric from a roll or sheet of stock material.
LO A–1
Use Microsoft Excel
Solver to solve a linear
programming problem.
Linear programming
(LP)
Refers to several
related mathematical
techniques used
to allocate limited
resources among
competing demands in
an optimal way.
691
692
APPENDIX A
Inventory control: Finding the optimal combination of products to stock in a network of
warehouses or storage locations.
Distribution scheduling: Finding the optimal shipping schedule for distributing products
between factories and warehouses or between warehouses and retailers.
Plant location studies: Finding the optimal location of a new plant by evaluating shipping
costs between alternative locations and supply and demand sources.
Material handling: Finding the minimum-cost routings of material-handling devices (such
as forklift trucks) between departments in a plant, or, for example, hauling materials from
a supply yard to work sites by trucks. Each truck might have different capacities and performance capabilities.
Linear programming is gaining wide acceptance in many industries due to the availability of detailed operating information and the interest in optimizing processes to reduce cost.
Many software vendors offer optimization options to be used with enterprise resource planning systems. Some firms refer to these as advanced planning option, synchronized planning,
and process optimization.
For linear programming to pertain in a problem situation, five essential conditions
must be met. First, there must be limited resources (such as a limited number of workers,
equipment, finances, and material); otherwise, there would be no problem. Second, there
must be an explicit objective (such as maximize profit or minimize cost). Third, there
must be linearity (two is twice as much as one; if three hours are needed to make a part,
then two parts would take six hours and three parts would take nine hours). Fourth, there
must be homogeneity (the products produced on a machine are identical, or all the hours
available from a worker are equally productive). Fifth, there must be divisibility: Normal
linear programming assumes products and resources can be subdivided into fractions.
If this subdivision is not possible (such as flying half an airplane or hiring one-fourth
of a person), a modification of linear programming, called integer programming, can
be used.
When a single objective is to be maximized (like profit) or minimized (like costs), we
can use linear programming. When multiple objectives exist, goal programming is used. If
a problem is best solved in stages or time frames, dynamic programming is employed. Other
restrictions on the nature of the problem may require that it be solved by other variations of
the technique, such as nonlinear programming or quadratic programming.
The Linear Programming Model
Stated formally, the linear programming problem entails an optimizing process in which nonnegative values for a set of decision variables X1, X2, . . . , Xn are selected so as to maximize (or
minimize) an objective function in the form
Maximize (minimize) Z = C1X1 + C2X2 + . . . + CnXn
subject to resource constraints in the form
​ 11
A
​ ​​X1​​+ ​A12
​ ​​X2​​+ . . . +​A1n
​ ​​Xn​​≤ ​B1​​
​A21
​ ​​X1​​+ ​A22
​ ​​X2​​+ . . . +​A2n
​ ​​Xn​​≤ ​B2​​
.
​​ ​
​ ​​
.
.
​Am1
​ ​​X1​​+ ​Am2
​ ​​X2​​+ . . . +​Amn
​ ​​Xn​​≤ ​Bm​ ​
where Cn, Amn, and Bm are given constants.
Depending on the problem, the constraints also may be stated with equal signs (=) or
greater-than-or-equal-to signs (≥).
693
APPENDIX A
EXAMPLE A.1: Puck and Pawn Company
We describe the steps involved in solving a simple linear programming model in the context
of a sample problem, that of Puck and Pawn Company, which manufactures hockey sticks
and chess sets. Each hockey stick yields an incremental profit of $2, and each chess set, $4.
A hockey stick requires 4 hours of processing at machine center A and 2 hours at machine
center B. A chess set requires 6 hours at machine center A, 6 hours at machine center B, and
1 hour at machine center C. Machine center A has a maximum of 120 hours of available
capacity per day, machine center B has 72 hours, and machine center C has 10 hours.
If the company wishes to maximize profit, how many hockey sticks and chess sets should
be produced per day?
SOLUTION
Formulate the problem in mathematical terms. If H is the number of hockey sticks and C is
the number of chess sets, to maximize profit the objective function may be stated as
Maximize Z = $2H + $4C
The maximization will be subject to the following constraints:
4H + 6C ≤ 120 (machine center A constraint )
2H + 6C ≤ 72 (machine center B constraint )
​
​​
1C ≤ 10 (machine center C constraint )
H, C ≤ 0
This formulation satisfies the five requirements for standard LP stated in the first section
of this appendix:
1.
2.
3.
4.
5.
There are limited resources (a finite number of hours available at each machine center).
There is an explicit objective function (we know what each variable is worth and what
the goal is in solving the problem).
The equations are linear (no exponents or cross-products).
The resources are homogeneous (everything is in one unit of measure, machine hours).
The decision variables are divisible and nonnegative (we can make a fractional part of
a hockey stick or chess set; however, if this were deemed undesirable, we would have
to use integer programming).
Graphical Linear Programming
Though limited in application to problems involving two decision variables (or three variables
for three-dimensional graphing), graphical linear programming provides a quick insight into
the nature of linear programming. We describe the steps involved in the graphical method in the
context of Puck and Pawn Company. The following steps illustrate the graphical approach.
1.
2.
3.
Formulate the problem in mathematical terms. The equations for the problem are
given previously.
Plot constraint equations. The constraint equations are easily plotted by letting one
variable equal zero and solving for the axis intercept of the other. (The inequality portions
of the restrictions are disregarded for this step.) For the machine center A constraint equation, when H = 0, C = 20, and when C = 0, H = 30. For the machine center B constraint
equation, when H = 0, C = 12, and when C = 0, H = 36. For the machine center C constraint equation, C = 10 for all values of H. These lines are graphed in Exhibit A.1.
Determine the area of feasibility. The direction of inequality signs in each constraint
determines the area where a feasible solution is found. In this case, all inequalities are
of the less-than-or-equal-to variety, which means it would be impossible to produce any
Graphical linear
programming
Provides a quick insight
into the nature of linear
programming.
694
APPENDIX A
Graph of Hockey Stick and Chess Set Problem
exhibit A .1
30
Infeasible region
4H + 6C = 120 (1)
20
Chess
sets per
day
12
10
C = 10 (3)
(3)
8
(2)
4
a
10
4.
Objective
function
lines
2H + 4C = $64
2H + 4C = $32
16
Feasible
region
Optimum
2H + 6C = 72 (2)
(1)
16
20
24
Hockey sticks per day
30
32
36
combination of products that would lie to the right of any constraint line on the graph. The
region of feasible solutions is unshaded on the graph and forms a convex polygon. A convex polygon exists when a line drawn between any two points in the polygon stays within
the boundaries of that polygon. If this condition of convexity does not exist, the problem
is either incorrectly set up or is not amenable to linear programming.
Plot the objective function. The objective function may be plotted by assuming some
arbitrary total profit figure and then solving for the axis coordinates, as was done for
the constraint equations. Other terms for the objective function when used in this context are the iso-profit or equal contribution line, because it shows all possible production combinations for any given profit figure. For example, from the dotted line closest
to the origin on the graph, we can determine all possible combinations of hockey sticks
and chess sets that yield $32 by picking a point on the line and reading the number of
each product that can be made at that point. The combination yielding $32 at point a
would be 10 hockey sticks and three chess sets. This can be verified by substituting
H = 10 and C = 3 in the objective function:
$2(10) + $4(3) = $20 + $12 = $32
H
C
0
120/4 = 30
0
72/2 = 36
0
0
32/2 = 16
0
64/2 = 32
120/6 = 20
0
72/6 = 12
0
10
32/4 = 8
0
64/4 = 16
0
5.
Explanation
Intersection of Constraint (1) and C axis
Intersection of Constraint (1) and H axis
Intersection of Constraint (2) and C axis
Intersection of Constraint (2) and H axis
Intersection of Constraint (3) and C axis
Intersection of $32 iso-profit line (objective function) and C axis
Intersection of $32 iso-profit line and H axis
Intersection of $64 iso-profit line and C axis
Intersection of $64 iso-profit line and H axis
Find the optimum point. It can be shown mathematically that the optimal combination
of decision variables is always found at an extreme point (corner point) of the convex
polygon. In Exhibit A.1, there are four corner points (excluding the origin), and we can
determine which one is the optimum by either of two approaches. The first approach is
to find the values of the various corner solutions algebraically. This entails simultaneously solving the equations of various pairs of intersecting lines and substituting the
APPENDIX A
quantities of the resultant variables in the objective function. For example, the calculations for the intersection of 2H + 6C = 72 and C = 10 are as follows:
Substituting C = 10 in 2H + 6C = 72 gives 2H + 6(10) = 72, 2H = 12, or H = 6. Substituting H = 6 and C = 10 in the objective function, we get
Profit = $2H + $4C = $2​​(​6​)​+ $4​​(​10​)​
​
​ ​
​
​
= $12 + $40 = $52
A variation of this approach is to read the H and C quantities directly from the graph and
substitute these quantities into the objective function, as shown in the previous calculation.
The drawback in this approach is that, in problems with a large number of constraint equations, there will be many possible points to evaluate, and the procedure of testing each one
mathematically is inefficient.
The second and generally preferred approach entails using the objective function or isoprofit line directly to find the optimum point. The procedure involves simply drawing a
straight line parallel to any arbitrarily selected initial iso-profit line so the iso-profit line is
farthest from the origin of the graph. (In cost minimization problems, the objective would
be to draw the line through the point closest to the origin.) In Exhibit A.1, the dashed line
labeled $2H + $4C = $64 intersects the most extreme point. Note that the initial arbitrarily
selected iso-profit line is necessary to display the slope of the objective function for the
particular problem. (Note, the slope of the objective function is –2. If P = profit, P = $2H
+ $4C; $2H = P + $4C; H = P/2 – 2C. Thus, the slope is –2.) This is important because a
different objective function (try Profit = 3H + 3C) might indicate that some other point is
farthest from the origin. Given that $2H + $4C = $64 is optimal, the amount of each variable to produce can be read from the graph: 24 hockey sticks and four chess sets. No other
combination of the products yields a greater profit.
Linear Programming Using Microsoft Excel
Spreadsheets can be used to solve linear programming problems. Microsoft Excel has an
optimization tool called Solver that we will demonstrate by solving the hockey stick and
chess problem. We invoke the Solver from the Data tab. A dialogue box requests information
required by the program. The following example describes how our sample problem can be
solved using Excel.
If the Solver option does not appear in your Data tab, click on File → Options → Add-Ins
→ Go (Manage Excel Add-Ins) → Select the Solver Add-in. Solver should then be available
directly from the Data tab for future use.
In the following example, we work in a step-by-step manner, setting up a spreadsheet and then
solving our Puck and Pawn Company problem. Our basic strategy is to first define the problem
within the spreadsheet. Following this, we invoke the Solver and feed it required information.
Finally, we execute the Solver and interpret results from the reports provided by the program.
S t e p 1 : D e f i n e C h a n g i n g C e l l s A convenient starting point is to identify cells
to be used for the decision variables in the problem. These are H and C, the number of hockey
sticks and the number of chess sets to produce. Excel refers to these cells as changing cells in
Solver. Referring to our Excel screen (Exhibit A.2), we have designated B4 as the location for
the number of hockey sticks to produce and C4 for the number of chess sets. Note that we have
set these cells equal to two initially. We could set these cells to anything, but a value other
than zero will help verify that our calculations are correct.
S t e p 2 : C a l c u l a t e T o t a l P r o f i t ( o r C o s t ) This is our objective function
and is calculated by multiplying profit associated with each product by the number of units
produced. We have placed the profits in cells B5 and C5 ($2 and $4), so the profit is calculated
by the following equation: B4*B5 + C4*C5, which is calculated in cell D5. Solver refers to
this as the Target Cell, and it corresponds to the objective function for a problem.
695
696
APPENDIX A
exhibit A .2
Microsoft Excel Screen for Puck and Pawn Company
© McGraw-Hill Education
S t e p 3 : S e t U p R e s o u r c e U s a g e Our resources are machine centers A, B,
and C as defined in the original problem. We have set up three rows (9, 10, and 11) in our
spreadsheet, one for each resource constraint. For machine center A, 4 hours of processing
time are used for each hockey stick produced (cell B9) and 6 hours for each chess set (cell C9).
For a particular solution, the total amount of the machine center A resource used is calculated
in D9 (B9*B4 + C9*C4). We have indicated in cell E9 that we want this value to be less
than the 120-hour capacity of machine center A, which is entered in F9. Resource usage for
machine centers B and C is set up in the exact same manner in rows 10 and 11.
S t e p 4 : S e t U p S o l v e r Go to the Data tab and select the Solver option.
1.
2.
3.
4.
5.
APPENDIX A
Set Objective: is set to the location where the value that we want to optimize is calculated. This is the profit calculated in D5 in our spreadsheet.
To: is set to Max because the goal is to maximize profit.
By Changing Variable Cells: are the cells that Solver can change to maximize profit.
Cells B4 through C4 are the changing cells in our problem.
Subject to the Constraints: corresponds to our machine center capacity. Here we click on
Add and indicate that the total used for a resource is less than or equal to the capacity available. A sample for machine center A follows. Click OK after each constraint is specified.
Select a Solving Method allows us to tell Solver what type of problem we want it to solve
and how we want it solved. Solver has numerous options, but we will need to use only a few.
Most of the options relate to how Solver attempts to solve nonlinear problems. These can be
very difficult to solve, and optimal solutions difficult to find. Luckily, our problem is a linear
problem. We know this because our constraints and our objective function are all calculated
using linear equations. Select Simplex LP to tell Solver that we want to use the linear programming option for solving the problem. In addition, we know our changing cells (decision variables) must be numbers that are greater than or equal to zero because it makes no sense to create
a negative number of hockey sticks or chess sets. We indicate this by selecting Make Unconstrained Variables Non-Negative as an option. We are now ready to actually solve the problem.
S t e p 5 : S o l v e t h e P r o b l e m Click Solve. We immediately get a Solver Results
acknowledgment like that shown as follows.
Solver acknowledges that a solution was found that appears to be optimal. On the right side of this
box are options for three reports: an Answer Report, a Sensitivity Report, and a Limits Report. Click
on each report to have Solver provide these. After highlighting the reports, click OK to exit back to
the spreadsheet. Three new tabs have been created that correspond to these reports.
697
698
APPENDIX A
exhibit A .3
Excel Solver Answer and Sensitivity Reports
Answer Report
Target Cell (Max)
Cell
Name
$D$5
Profit Total
Original Value
Final Value
$12
$64
Original Value
Final Value
Adjustable Cells
Cell
Name
$B$4
Changing Cells Hockey Sticks
2
24
$C$4
Changing Cells Chess Sets
2
4
Constraints
Cell
Name
$D$11
Machine C Used
$D$10
$D$9
Cell Value
Formula
Status
Slack
4
$D$1<=$F$11
Not Binding
6
Machine B Used
72
$D$10<=$F$10
Binding
0
Machine A Used
120
$D$9<=$F$9
Binding
0
Sensitivity Report
Adjustable Cells
Final
Value
Reduced
Cost
Objective
Coefficient
Allowable
Increase
Allowable
Decrease
Changing Cells Hockey
Sticks
24
0
2
0.666666667
0.666666667
Changing Cells Chess
Sets
4
0
4
2
1
Final
Value
Shadow
Price
Constraint
R.H. Side
Allowable
Increase
Cell
Name
$B$4
$C$4
Constraints
Allowable
Decrease
Cell
Name
$D$11
Machine C Used
4
0
10
1E + 30
$D$10
Machine B Used
72
0.333333333
72
18
12
$D$9
Machine A Used
120
0.333333333
120
24
36
6
The most interesting reports for our problem are the Answer Report and the Sensitivity
Report, both of which are shown in Exhibit A.3. The Answer Report shows the final answers
for the total profit ($64) and the amounts produced (24 hockey sticks and 4 chess sets). In the
constraints section of the Answer Report, the status of each resource is given. All of machine
A and machine B are used, and there are six units of slack for machine C.
The Sensitivity Report is divided into two parts. The first part, titled “Adjustable
Cells,” corresponds to objective function coefficients. The profit per unit for the hockey
sticks can be either up or down $0.67 (between $2.67 and $1.33) without having an
impact on the solution. Similarly, the profit of the chess sets could be between $6 and
$3 without changing the solution. In the case of machine A, the right-hand side could
increase to 144 (120 + 24) or decrease to 84 with a resulting $0.33 increase or decrease
per unit in the objective function. The right-hand side of machine B can increase to
90 units or decrease to 60 units with the same $0.33 change for each unit in the objective function. For machine C, the right-hand side could increase to infinity (1E + 30 is
scientific notation for a very large number) or decrease to 4 units with no change in the
objective function.
699
APPENDIX A
Concept Connections
LO A–1: Use Microsoft Excel Solver to solve a linear programming problem.
Summary
∙ Linear programming is a powerful tool for today’s
business because it allows managers to make the best
use of the available resources of material, plant, and
equipment.
∙ Using Microsoft Excel Solver, we can solve linear programming problems dealing with aggregate
sales and operations planning, service/manufacturing
productivity analysis, product planning, product routing, and more.
∙ Linear programming problems can be solved in Microsoft Excel Solver using the following steps: (1) Define
changing cells; (2) Calculate total profit (or cost); (3)
Set up resource usage; (4) Set up the Solver; (5) Solve
the problem.
Key Terms
Linear programming (LP) Refers to several related math-
ematical techniques used to allocate limited resources
among competing demands in an optimal way.
Graphical linear programming Provides a quick insight
into the nature of linear programming.
Solved Problem
SOLVED PROBLEM 1
A furniture company produces three products: end tables, sofas, and chairs. These products are
processed in five departments: the saw lumber, fabric cutting, sanding, staining, and assembly
departments. End tables and chairs are produced from raw lumber only, and the sofas require
lumber and fabric. Glue and thread are plentiful and represent a relatively insignificant cost
that is included in operating expense. The specific requirements for each product are as follows.
Resource or Activity
(quantity available
per month)
Required per
End Table
Required
per Sofa
Required per
Chair
Lumber (4,350 board feet)
10 board feet @
7.5 board feet @
$10/foot = $100/table
$10/foot = $75
4 board feet @
$10/foot = $40
Fabric (2,500 yards)
None
10 yards @ $17.50/yard = $175
None
Saw lumber (280 hours)
30 minutes
24 minutes
30 minutes
Cut fabric (140 hours)
None
24 minutes
None
Sand (280 hours)
30 minutes
6 minutes
30 minutes
Stain (140 hours)
24 minutes
12 minutes
24 minutes
Assemble (700 hours)
60 minutes
90 minutes
30 minutes
The company’s direct labor expenses are $75,000 per month for the 1,540 hours of labor, at $48.70
per hour. Based on current demand, the firm can sell 300 end tables, 180 sofas, and 400 chairs per
month. Sales prices are $400 for end tables, $750 for sofas, and $240 for chairs. Assume that labor
cost is fixed and the firm does not plan to hire or fire any employees over the next month.
Required:
1. What is the most limiting resource to the furniture company?
2. Determine the product mix needed to maximize profit at the company. What is the optimal
number of end tables, sofas, and chairs to produce each month?
Solution
Define X1 as the number of end tables, X2 as the number of sofas, and X3 as the number of
chairs to produce each month. Profit is calculated as the revenue for each item minus the cost
700
APPENDIX A
of materials (lumber and fabric), minus the cost of labor. Because labor is fixed, we subtract
this out as a total sum. Mathematically, we have (400 – 100)X1 + (750 – 75 – 175)X2 + (240 –
40)X3 – 75,000. Profit is calculated as follows:
Profit = 300X1 + 500X2 + 200X3 – 75,000
Constraints are the following:
Lumber:
Fabric:
Saw:
Cut:
Sand:
Stain:
Assemble:
Demand:
Table:
Sofa:
Chair:
10X1 + 7.5X2 + 4X3 ≤ 4,350
10X2 ≤ 2,500
.5X1 + .4X2 + .5X3 ≤ 280
.4X2 ≤ 140
.5X1 + .1X2 + .5X3 ≤ 280
.4X1 + .2X2 + .4X3 ≤ 140
1X1 + 1.5X2 + .5X3 ≤ 700
X1 ≤ 300
X2 ≤ 180
X3 ≤ 400
Step 1: Define Changing Cells These are B3, C3, and D3. Note that these cells have
been set equal to zero.
Step 2: Calculate Total Profit This is E4 (this is equal to B3 times the $300 revenue
associated with each end table, plus C3 times the $500 revenue for each sofa, plus D3 times
the $200 revenue associated with each chair). Note the $75,000 fixed expense that has been
subtracted from revenue to calculate profit.
Step 3: Set Up Resource Usage In cells E6 through E15, the usage of each resource is
calculated by multiplying B3, C3, and D3 by the amount needed for each item and summing
the product (for example, E6 = B3*B6 + C3*C6 + D3*D6). The limits on these constraints
are entered in cells G6 to G15.
APPENDIX A
701
Step 4: Set Up Solver Go to Tools and select the Solver option.
a. Set Objective: is set to the location where the value that we want to optimize is calculated. This is the profit calculated in E4 in this spreadsheet.
b. To: is set to Max because the goal is to maximize profit.
c. By Changing Variable Cells: are the cells that Solver can change to maximize profit
(cells B3 through D3 in this problem).
d. Subject to the Constraints: is where a constraint set is added; we indicate that the
range E6 to E15 must be less than or equal to G6 to G15.
Step 5: Select a Solving Method There are a few options here, but for our purposes we
just need to indicate Simplex LP and Make Unconstrained Variables Non-Negative. Simplex
LP means all of our formulas are simple linear equations. Make Unconstrained Variables
Non-Negative indicates that changing cells must be greater than or equal to zero.
Step 6: Solve the Problem Click Solve. We can see the solution and two special reports
by highlighting items on the Solver Results acknowledgment that is displayed after a solution
is found. Note that in the following report, Solver indicates that it has found a solution and
all constraints and optimality conditions are satisfied. In the Reports box on the right, the
702
APPENDIX A
Answer, Sensitivity, and Limits options have been highlighted, indicating we would like to
see these items. After highlighting the reports, click OK to exit back to the spreadsheet.
Note that three new tabs have been created: an Answer Report, a Sensitivity Report, and a
Limits Report. The Answer Report indicates in the Target Cell section that the profit associated with this solution is $93,000 (we started at –$75,000). From the Target Cell section, we
should make 260 end tables, 180 sofas, and no chairs. From the Constraints section, notice
that the only constraints limiting profit are the staining capacity and the demand for sofas. We
can see this from the column indicating whether a constraint is binding or nonbinding. Nonbinding constraints have slack, as indicated in the last column.
Target Cell (Max)
Cell
Name
$E$4
Profit Total
Original Value
Final Value
−$75,000
$93,000
Adjustable Cells
Cell
Name
Original Value
Final Value
$B$3
Changing cells End Tables
0
260
$C$3
Changing cells Sofas
0
180
$D$3
Changing cells Chairs
0
0
Constraints
Cell
Name
Cell Value
Formula
$E$6
$E$7
$E$8
Saw Total
$E$9
Cut fabric Total
$E$10
Sand Total
$E$11
Stain Total
$E$12
$E$13
Status
Slack
Lumber Total
3950
$E$6<=$G$6
Not Binding
400
Fabric Total
1800
$E$7<=$G$7
Not Binding
700
202
$E$8<=$G$8
Not Binding
78
72
$E$9<=$G$9
Not Binding
68
148
$E$10<=$G$10
Not Binding
132
140
$E$1<=$G$11
Binding
Assemble Total
530
$E$12<=$G$12
Not Binding
170
Table Demand Total
260
$E$13<=$G$13
Not Binding
40
$E$14
Sofa Demand Total
180
$E$14<=$G$14
Binding
$E$15
Chair Demand Total
0
$E$15<=$G$15
Not Binding
0
0
400
703
APPENDIX A
Of course, we may not be too happy with this solution because we are not meeting all
the demand for tables, and it may not be wise to totally discontinue the manufacturing of
chairs.
The Sensitivity Report (shown as follows) gives additional insight into the solution.
The Adjustable Cells section of this report shows the final value for each cell and the
reduced cost. The reduced cost indicates how much the target cell value would change if
a cell that was currently set to zero were brought into the solution. Because the end tables
(B3) and sofas (C3) are in the current solution, their reduced cost is zero. For each chair
(D3) we make, our target cell would be reduced $100 (just round these numbers for interpretation purposes). The final three columns in the adjustable cells section of the report
are the Objective Coefficient from the original spreadsheet and columns titled Allowable
Increase and Allowable Decrease. Allowable Increase and Decrease show by how much
the value of the corresponding coefficient could change so there would not be a change
in the changing cell values (of course, the target cell value would change). For example,
revenue for each end table could be as high as $1,000 ($300 + $700) or as low as $200
($300 – $100), and we would still want to produce 260 end tables. Keep in mind that these
values assume nothing else is changing in the problem. For the allowable increase value
for sofas, note the value 1E + 30. This is a very large number, essentially infinity, represented in scientific notation.
Adjustable Cells
Final
Value
Cell
Name
$B$3
Changing cells End Tables
260
$C$3
Changing cells Sofas
180
$D$3
Changing cells Chairs
0
Reduced
Cost
Objective
Coefficient
Allowable
Increase
Allowable
Decrease
0
299.9999997
700.0000012
100.0000004
0
500.0000005
1E + 30
350.0000006
−100.0000004
199.9999993
100.0000004
1E + 30
Constraints
Cell
Name
Final
Value
Shadow
Price
$E$6
Lumber Total
3950
0
4350
1E + 30
400
$E$7
Fabric Total
1800
0
2500
1E + 30
700
$E$8
Saw Total
202
0
280
1E + 30
78
$E$9
Cut fabric Total
72
0
140
1E + 30
68
$E$10
Sand Total
148
0
280
1E + 30
132
$E$11
Stain Total
140
140
16
104
$E$12
Assemble Total
530
0
700
1E + 30
170
$E$13
Table Demand Total
260
0
300
1E + 30
40
$E$14
Sofa Demand Total
180
180
70
80
$E$15
Chair Demand Total
400
1E + 30
400
749.9999992
350.0000006
0
0
Constraint
R.H. Side
Allowable
Increase
Allowable
Decrease
For the Constraints section of the report, the actual final usage of each resource is given
in Final Value. The Shadow Price is the value to our target cell for each unit increase in the
resource. If we could increase staining capacity, it would be worth $750 per hour. The Constraint Right-Hand Side is the current limit on the resource. Allowable Increase is the amount
the resource could be increased while the shadow price is still valid. Another 16 hours’ work
of staining capacity could be added with a value of $750 per hour. Similarly, the Allowable Decrease column shows the amount the resource could be reduced without changing the
shadow price. There is some valuable information available in this report.
The Limits Report provides additional information about our solution.
Cell
Target Name
Value
$E$4
Profit Total
$93,000
704
APPENDIX A
Lower
Limit
Target
Result
Upper Limit
Target
Result
260
0
15000
260.0000002
93000
180
0
3000
180
93000
0
0
93000
0
93000
Cell
Adjustable Name
Value
$B$3
Changing cells End Tables
$C$3
Changing cells Sofas
$D$3
Changing cells Chairs
Total profit for the current solution is $93,000. Current value for B3 (end tables) is 260
units. If this were reduced to 0 units, profit would be reduced to $15,000. At an upper limit
of 260, profit is $93,000 (the current solution). Similarly, for C3 (sofas), if this were reduced
to 0, profit would be reduced to $3,000. At an upper limit of 180, profit is $93,000. For D3
(chairs), if this were reduced to 0, profit is $93,000 (current solution), and in this case the
upper limit on chairs is also 0 units.
Acceptable answers to the questions are as follows:
1. What is the most limiting resource to the furniture company?
In terms of our production resources, staining capacity is really hurting profit at this time.
We could use another 16 hours of capacity.
2. Determine the product mix needed to maximize profit at the furniture company.
The product mix would be to make 260 end tables, 180 sofas, and no chairs.
Of course, we have only scratched the surface with this solution. We could actually
experiment with increasing staining capacity. This would give insight into the next most limiting resource. We also could run scenarios where we are required to produce a minimum number of each product, which is probably a more realistic scenario. This could help us determine
how we could possibly reallocate the use of labor in our shop.
SOLVED PROBLEM 2
It is 2:00 on Friday afternoon and Joe Bob, the head chef (grill cook) at Bruce’s Diner, is
trying to decide the best way to allocate the available raw material to the four Friday night
specials. The decision has to be made in the early afternoon because three of the items must
be started now (Sloppy Joes, Tacos, and Chili). The following table contains the information
on the food in inventory and the amounts required for each item.
Food
Cheeseburgers
Sloppy Joes
Tacos
Chili
Available
Ground Beef (lbs.)
0.3
0.25
0.25
0.4
100 lbs.
Cheese (lbs.)
0.1
0
0.3
0.2
50 lbs.
Beans (lbs.)
0
0
0.2
0.3
50 lbs.
Lettuce (lbs.)
0.1
0
0.2
0
15 lbs.
Tomato (lbs.)
0.1
0.3
0.2
0.2
50 lbs.
Buns
1
1
0
0
80 buns
Taco Shells
0
0
1
0
80 shells
One other fact relevant to Joe Bob’s decision is the estimated market demand and selling
price.
Cheeseburgers
Demand
Selling Price
Sloppy Joes
Tacos
Chili
75
60
100
55
$2.25
$2.00
$1.75
$2.50
Joe Bob wants to maximize revenue because he has already purchased all the materials that
are sitting in the cooler.
Required:
1. What is the best mix of the Friday night specials to maximize Joe Bob’s revenue?
2. If a supplier offered to provide a rush order of buns at $1.00 a bun, is it worth the money?
APPENDIX A
705
SOLUTION
Define X1 as the number of Cheeseburgers, X2 as the number of Sloppy Joes, X3 as the number
of Tacos, and X4 as the number of bowls of Chili made for the Friday night specials.
Revenue = $2.25 X1 + $2.00 X2 + $1.75 X3 + $2.50 X4
Constraints are the following:
Ground Beef:
Cheese:
Beans:
Lettuce:
Tomato:
Buns:
Taco Shells:
Demand
Cheeseburger
Sloppy Joes
Tacos
Chili
0.30 X1 + 0.25 X2 + 0.25 X3 + 0.40 X4 ≤ 100
0.10 X1 + 0.30 X3 + 0.20 X4 ≤ 50
0.20 X3 + 0.30 X4 ≤ 50
0.10 X1 + 0.20 X3 ≤ 15
0.10 X1 + 0.30 X2 + 0.20 X3 + 0.20 X4 ≤ 50
X1 + X2 ≤ 80
X3 ≤ 80
X1 ≤ 75
X2 ≤ 60
X3 ≤ 100
X4 ≤ 55
Step 1: Define the Changing Cells These are B3, C3, D3, and E3. Note the values in
the changing cell are set to 10 each so the formulas can be checked.
Step 2: Calculate Total Revenue This is in cell F7 (this is equal to B3 times the $2.25
for each Cheeseburger, plus C3 times the $2.00 for a Sloppy Joe, plus D3 times the $1.75 for
each Taco, plus E3 times the $2.50 for each bowl of Chili; the SUMPRODUCT function in
706
APPENDIX A
Excel was used to make this calculation faster). Note that the current value is $85, which is a
result of selling 10 of each item.
Step 3: Set Up the Usage of the Food In cells F11 to F17, the usage of each food is
calculated by multiplying the changing cells row times the per item use in the table and then
summing the result. The limits on each of these food types are given in H11 through H17.
Step 4: Set Up Solver and Select the Solver Option
a. Set Objective: is set to the location where the value that we want to optimize is calculated. The revenue is calculated in F7 in this spreadsheet.
b. To: is set to Max because the goal is to maximize revenue.
c. By Changing Variable Cells: are the cells that tell how many of each special to
produce.
d. Subject to the Constraints: is where we add two separate constraints, one for demand
and one for the usage of food.
Step 5: Select a Solving Method We will leave all the settings as the default values and
only make sure of two changes: (1) Simplex LP option and (2) check the Make Unconstrained
Variables Non-Negative. These two options make sure that Solver knows that this is a linear
programming problem and that all changing cells should be nonnegative.
707
APPENDIX A
Step 6: Solve the Problem Click Solve. We will get a Solver Results box. Make sure it
says it has the following statement: “Solver found a solution. All constraints and optimality
conditions are satisfied.”
On the right-hand side of the box, there is an option for three reports: Answer, Sensitivity, and Limit. Click on all three reports and then click OK. This will exit you back to the
spreadsheet, but you will have three new worksheets in your workbook.
The answer report indicates that the target cell has a final solution of $416.25 and started
at $85. From the adjustable cells area, we can see that we should make 20 Cheeseburgers,
60 Sloppy Joes, 65 Tacos, and 55 bowls of Chili. This answers the first requirement from the
problem of what the mix of Friday night specials should be.
Target Cell (Max)
Cell
Name
$F$7
Revenue Total
Original Value
Final Value
$85.00
$416.25
Original Value
Final Value
Adjustable Cells
Cell
Name
$B$3
Changing Cells Cheeseburgers
10
20
$C$3
Changing Cells Sloppy Joes
10
60
$D$3
Changing Cells Tacos
10
65
$E$3
Changing Cells Chili
10
55
Constraints
Cell
Name
Formula
Status
Slack
$F$11
Ground Beef (lbs.) Total
Cell Value
59.25
$F$11<=$H$11
Not Binding
40.75
$F$12
Cheese (lbs.) Total
32.50
$F$12<=$H$12
Not Binding
17.5
$F$13
Beans (lbs.) Total
29.50
$F$13<=$H$13
Not Binding
20.5
$F$14
Lettuce (lbs.) Total
15.00
$F$14<=$H$14
Binding
0
$F$15
Tomato (lbs.) Total
44.00
$F$15<=$H$15
Not Binding
6
$F$16
Buns Total
80.00
$F$16<=$H$16
Binding
0
$F$17
Taco Shells Total
65.00
$F$17<=$H$17
Not Binding
15
$B$3
Changing Cells Cheeseburgers
20
$B$3<=$B$5
Not Binding
55
$C$3
Changing Cells Sloppy Joes
60
$C$3<=$C$5
Binding
0
$D$3
Changing Cells Tacos
65
$D$3<=$D$5
Not Binding
35
$E$3
Changing Cells Chili
55
$E$3<=$E$5
Binding
0
708
APPENDIX A
The second required answer was whether it is worth it to pay a rush supplier $1 a bun for
additional buns. The answer report shows us that the buns constraint was binding. This means
that if we had more buns, we could make more money. However, the answer report does not
tell us whether a rush order of buns at $1 a bun is worthwhile. In order to answer that question, we have to look at the sensitivity report.
Adjustable Cells
Final
Value
Reduced
Cost
Objective
Coefficient
Cell
Name
$B$3
Changing Cells Cheeseburgers
20
0
2.25
$C$3
Changing Cells Sloppy Joes
60
0.625
2
$D$3
Changing Cells Tacos
65
0
1.75
$E$3
Changing Cells Chili
55
2.5
2.5
Allowable
Increase
Allowable
Decrease
0.625
1.375
1E + 30
0.625
2.75
1E + 30
1.25
2.5
Constraints
Cell
Name
Final
Value
Shadow
Price
$F$11
Ground Beef (lbs.) Total
59.25
0.00
$F$12
Cheese (lbs.) Total
32.50
0.00
$F$13
Beans (lbs.) Total
29.50
$F$14
Lettuce (lbs.) Total
$F$15
Constraint
R.H. Side
Allowable
Increase
Allowable
Decrease
100
1E + 30
40.75
50
1E + 30
17.5
0.00
50
1E + 30
20.5
15.00
8.75
15
3
13
Tomato (lbs.) Total
44.00
0.00
50
1E + 30
6
$F$16
Buns Total
80.00
1.38
80
55
20
$F$17
Taco Shells Total
65.00
0.00
80
1E + 30
15
We have highlighted the buns row to answer the question. We can see that buns have a
shadow price of $1.38. This shadow price means that each additional bun will generate $1.38
of profit. We also can see that other foods such as ground beef have a shadow price of $0. The
items with a shadow price of $0 add nothing to profit because we are currently not using all
that we have now. The other important piece of information that we have on the buns is that
they are only worth $1.38 up until the next 55 buns, and that is why the allowable increase is
55. We also can see that a pound of lettuce is worth $8.75. It might be wise to also look for a
rush supplier of lettuce so we can increase our profit on Friday nights.
Acceptable answers to the questions are as follows:
1. What is the best mix of the Friday night specials to maximize Joe Bob’s revenue?
20 Cheeseburgers, 60 Sloppy Joes, 65 Tacos, and 55 bowls of Chili
2. If a supplier offered to provide a rush order of buns at $1.00 a bun, is it worth the money?
Yes, each additional bun brings in $1.38, so if they cost us $1, then we will net $0.38 per
bun. However, this is true only up to 55 additional buns.
Objective Questions
1. Solve the following problem with Excel Solver:
Maximize Z = 3X + Y.
12X + 14Y ≤ 85
​
​
​
​
3X + 2Y ≤ 18
Y ≤4
2. Solve the following problem with Excel Solver: (Answer in Appendix D)
Maximize Z = 2A + 4B.
4A + 6B ≥ 120
​
​
​​
​
2A + 6B ≥ 72
B ≥ 10
APPENDIX A
709
3. A manufacturing firm has discontinued production of a certain unprofitable product line.
Considerable excess production capacity was created as a result. Management is considering devoting this excess capacity to one or more of three products: X1, X2, and X3.
Machine hours required per unit are:
Product
Machine Type
X1
X2
X3
Milling machine
8
2
3
Lathe
4
3
0
Grinder
2
0
1
The available time in machine hours per week is:
Machine Hours per Week
Milling machines
800
Lathes
480
Grinders
320
The salespeople estimate they can sell all the units of X1 and X2 that can be made. But
the sales potential of X3 is 80 units per week maximum.
Unit profits for the three products are:
Unit Profits
X1
$20
X2
6
X3
8
a. Set up the equations that can be solved to maximize the profit per week.
b. Solve these equations using the Excel Solver.
c. What is the optimal solution? How many of each product should be made, and what
should the resultant profit be?
d. What is this situation with respect to the machine groups? Would they work at ­capacity,
or would there be unused available time? Will X3 be at maximum sales capacity?
e. Suppose an additional 200 hours per week can be obtained from the milling machines
by using staff overtime. The incremental cost would be $1.50 per hour. Would you
recommend doing this? Explain how you arrived at your answer.
4. A diet is being prepared for the University of Arizona dorms. The objective is to feed
the students at the least cost, but the diet must have between 1,800 and 3,600 calories.
No more than 1,400 calories can be starch, and no fewer than 400 can be protein. The
varied diet is to be made of two foods: A and B. Food A costs $0.75 per pound and
contains 600 calories, 400 of which are protein and 200 starch. No more than two
pounds of food A can be used per resident. Food B costs $0.15 per pound and contains
900 calories, of which 700 are starch, 100 are protein, and 100 are fat. (Answers in
Appendix D)
a. Write the equations representing this information.
b. Solve the problem graphically for the amounts of each food that should be used.
5. Repeat problem 4 with the added constraint that not more than 150 calories shall be
fat and that the price of food has escalated to $1.75 per pound for food A and $2.50 per
pound for food B.
6. Logan Manufacturing wants to mix two fuels, A and B, for its trucks to minimize cost.
It needs no fewer than 3,000 gallons to run its trucks during the next month. It has a
maximum fuel storage capacity of 4,000 gallons. There are 2,000 gallons of fuel A and
4,000 gallons of fuel B available. The mixed fuel must have an octane rating of no less
than 80.
710
APPENDIX A
7.
8.
9.
10.
When fuels are mixed, the amount of fuel obtained is just equal to the sum of the
amounts put in. The octane rating is the weighted average of the individual octanes,
weighted in proportion to the respective volumes.
The following is known: Fuel A has an octane of 90 and costs $1.20 per gallon. Fuel B
has an octane of 75 and costs $0.90 per gallon.
a. Write the equations expressing this information.
b. Solve the problem using the Excel Solver, giving the amount of each fuel to be used.
State any assumptions necessary to solve the problem.
You are trying to create a budget to optimize the use of a portion of your disposable
income. You have a maximum of $1,500 per month to be allocated to food, shelter, and
entertainment. The amount spent on food and shelter combined must not exceed $1,000.
The amount spent on shelter alone must not exceed $700. Entertainment cannot exceed
$300 per month. Each dollar spent on food has a satisfaction value of 2, each dollar spent
on shelter has a satisfaction value of 3, and each dollar spent on entertainment has a satisfaction value of 5.
Assuming a linear relationship, use the Excel Solver to determine the optimal allocation of your funds.
C-Town Brewery brews two beers: Expansion Draft and Burning River. Expansion Draft
sells for $20 per barrel, while Burning River sells for $8 per barrel. Producing a barrel
of Expansion Draft takes 8 pounds of corn and 4 pounds of hops. Producing a barrel of
Burning River requires 2 pounds of corn, 6 pounds of rice, and 3 pounds of hops. The
brewery has 500 pounds of corn, 300 pounds of rice, and 400 pounds of hops. Assuming
a linear relationship, use Excel Solver to determine the optimal mix of Expansion Draft
and Burning River that maximizes C-Town’s revenue.
BC Petrol manufactures three chemicals at its chemical plant in Kentucky: BCP1, BCP2,
and BCP3. These chemicals are produced in two production processes known as zone
and man. Running the zone process for an hour costs $48 and yields three units of BCP1,
one unit of BCP2, and one unit of BCP3. Running the man process for one hour costs
$24 and yields one unit of BCP1 and one unit of BCP2. To meet customer demands, at
least 20 units of BCP1, 10 units of BCP2, and 6 units of BCP3 must be produced daily.
Assuming a linear relationship, use Excel Solver to determine the optimal mix of processes zone and man to minimize costs and meet BC Petrol daily demands.
A farmer in Wood County has 900 acres of land. She is going to plant each acre with
corn, soybeans, or wheat. Each acre planted with corn yields a $2,000 profit; each with
soybeans yields $2,500 profit; and each with wheat yields $3,000 profit. She has 100
workers and 150 tons of fertilizer. The following table shows the requirement per acre
of each of the crops. Assuming a linear relationship, use Excel Solver to determine the
optimal planting mix of corn, soybeans, and wheat to maximize her profits.
Corn
Soybeans
Wheat
Labor (workers)
0.1
0.3
0.2
Fertilizer (tons)
0.2
0.1
0.4
A PPENDIX B
O P E R AT I O N S T E C H N O LO G Y
Much of the recent growth in productivity has come from the application of operations technology. In services, this comes primarily from soft technology—information processing. In
manufacturing, it comes from a combination of soft and hard (machine) technologies. Given
that most readers of this book have covered information technologies in services in MIS
courses, our focus in this supplement is on manufacturing.
LO B–1
Explain how the
application of operations
technology has affected
manufacturing.
Te c h n o l o g i e s i n M a n u f a c t u r i n g
Some technological advances in recent decades have had a significant, widespread impact on
manufacturing firms in many industries. These advances, which are the topic of this section,
can be categorized in two ways: hardware systems and software systems.
Hardware technologies have generally resulted in greater automation of processes; they
perform labor-intensive tasks originally performed by humans. Examples of these major
types of hardware technologies are numerically controlled machine tools, machining centers,
industrial robots, automated materials handling systems, and flexible manufacturing systems.
These are all computer-controlled devices that can be used in the manufacturing of products.
Software-based technologies aid in the design of manufactured products and in the analysis
and planning of manufacturing activities. These technologies include computer-aided design
and automated manufacturing planning and control systems. Each of these technologies will
be described in greater detail in the following sections.
H a r d w a r e S y s t e m s Numerically controlled (NC) machines are comprised of (1) a
typical machine tool used to turn, drill, or grind different types of parts and (2) a computer
that controls the sequence of processes performed by the machine. NC machines were first
adopted by U.S. aerospace firms in the 1960s, and they have since proliferated to many
other industries. In more recent models, feedback control loops determine the position of the
machine tooling during the work, constantly compare the actual location with the programmed
location, and correct as needed. This is often called adaptive control.
Machining centers represent an increased level of automation and complexity relative to
NC machines. Machining centers not only provide automatic control of a machine, they also
may carry many tools that can be automatically changed depending on the tool required for
each operation. In addition, a single machine may be equipped with a shuttle system so that a
finished part can be unloaded and an unfinished part loaded while the machine is working on
a part. To help you visualize a machining center, we have included a diagram in Exhibit B.1A.
Industrial robots are used as substitutes for workers for many repetitive manual activities and tasks that are dangerous, dirty, or dull. A robot is a programmable, multifunctional
machine that may be equipped with an end effector. Examples of end effectors include a
gripper to pick things up or a tool such as a wrench, a welder, or a paint sprayer. Exhibit
B.1B examines the human motions a robot can reproduce. Advanced capabilities have been
designed into robots to allow vision, tactile sensing, and hand-to-hand coordination. In addition, some models can be “taught” a sequence of motions in a three-dimensional pattern. As
a worker moves the end of the robot arm through the required motions, the robot records this
pattern in its memory and repeats it on command. Newer robotic systems can conduct quality
control inspections and then transfer, via mobile robots, those parts to other robots downstream. As shown in the OSCM at Work box “Formula for Evaluating a Robot Investment,”
robots are often justified based on labor savings.
711
712
APPENDIX B
exhibit B.1
A. The CNC Machining Center
B. Typical Robot Axes of Motion
Tool changer
3
Cutting tool
1
3
Controller
Work piece
2
1
2
Jointed arm
1
3
2
Spherical coordinate
r
nge
cha
x
e
et
Cylindrical coordinate
3
l
Pal
1
2
Wrist axes
J. T. Black, The Design of the Factory with a Future (New York: McGraw-Hill,
1991), p. 39, with permission of The McGraw-Hill Companies.
L. V. Ottinger, “Robotics for the IE: Terminology, Types of Robots,” Industrial
Engineering, November 1981, p. 30.
Automated materials handing (AMH) systems improve efficiency of transportation, storage, and retrieval of materials. Examples are computerized conveyors and automated storage
and retrieval systems (AS/RS) in which computers direct automatic loaders to pick and place
items. Automated guided vehicle (AGV) systems use embedded floor wires to direct driverless vehicles to various locations in the plant. Benefits of AMH systems include quicker
material movement, lower inventories and storage space, reduced product damage, and higher
labor productivity.
OSCM AT WORK
Formula for Evaluating a Robot Investment
Many companies use the following modification of the
basic payback formula in deciding if a robot should be
purchased:
I
​P = ____________
​
​
L − E + q​​(​L + Z​)​
where
P = Payback period in years
I=
Total capital investment required in robot and
accessories
L = Annual labor costs replaced by the robot (wage
and benefit costs per worker times the number of
shifts per day)
E = Annual maintenance cost for the robot
q = Fractional speedup (or slowdown) factor
Z = Annual depreciation
Example:
I = $50,000
L = $60,000 (two workers × $20,000 each working
one of two shifts; overhead is $10,000 each)
E = $9,600 ($2/hour × 4,800 hours/year)
q = 1.5 (robot works 150 percent as fast as a worker)
Z = $10,000
then
$50, 000
P = ___________________________________
​    ​
​
​ ​ $60, 000 − $9, 600 + 1.5​​(​$60, 000 + $10, 000​)​
​ = 1 / 3 year
713
APPENDIX B
One of the four large
machining centers (see
Exhibit B.2) that are
part of the flexible
manufacturing systems
at Cincinnati Milacron’s
Mt. Orab, Ohio, Plant.
Courtesy of Cincinnati
Milacron, Mt. Orab, Ohio
plant
These individual pieces of automation can be combined to form manufacturing cells or
even complete flexible manufacturing systems (FMS). A manufacturing cell might consist
of a robot and a machining center. The robot could be programmed to automatically insert
and remove parts from the machining center, thus allowing unattended operation. An FMS is
a totally automated manufacturing system that consists of machining centers with the automated loading and unloading of parts, an automated guided vehicle system for moving parts
between machines, and other automated elements to allow the unattended production of parts.
In an FMS, a comprehensive computer control system is used to run the entire system.
A good example of an FMS is the Cincinnati Milacron facility in Mt. Orab, Ohio, which
has been in operation for over 30 years. Exhibit B.2 is a layout of this FMS. In this system,
parts are loaded onto standardized fixtures (these are called “risers”), which are mounted on
pallets that can be moved by the AGVs. Workers load and unload tools and parts onto the
standardized fixtures at the workstations shown on the right side of the diagram. Most of this
loading and unloading is done during a single shift. The system can operate virtually unattended for the other two shifts each day.
Within the system there are areas for the storage of tools (Area 7) and for parts (Area 5).
This system is designed to machine large castings used in the production of the machine tools
made by Cincinnati Milacron. The machining is done by the four CNC machining centers
(Area 1). When the machining has been completed on a part, it is sent to the parts washing
station (Area 4), where it is cleaned. The part is then sent to the automated inspection station
(Area 6) for a quality check. The system is capable of producing hundreds of different parts.
S o f t w a r e S y s t e m s Computer-aided design (CAD) is an approach to product and
process design that utilizes the power of the computer. CAD covers several automated
technologies, such as computer graphics to examine the visual characteristics of a product
and computer-aided engineering (CAE) to evaluate its engineering characteristics. Rubbermaid
used CAD to refine dimensions of its ToteWheels to meet airline requirements for checked
baggage. CAD also includes technologies associated with the manufacturing process design,
referred to as computer-aided process planning (CAPP). CAPP is used to design the computer
part programs that serve as instructions to computer-controlled machine tools and to design
the programs used to sequence parts through the machine centers and other processes (such
714
APPENDIX B
exhibit B.2
The Cincinnati Milacron Flexible Manufacturing System
12
8
2
3
1
4
9
13
7
6
5
11
Conference
room
10
Key:
1 Four Milacron T-30 CNC Machining
Centers.
2 Four tool interchange stations, one per
machine, for tool storage chain delivery
via computer-controlled cart.
3 Cart maintenance station. Coolant
monitoring and maintenance area.
4 Parts wash station, automatic handling.
5 Automatic Workchanger (10 pallets) for
online pallet queue.
6 One inspection module—horizontal type
coordinate measuring machine.
7 Three queue stations for tool delivery
chains.
8 Tool delivery chain load/unload stations.
9 Four part load/unload stations.
10 Pallet/fixture build station.
11 Control center, computer room (elevated).
12 Centralized chip/coolant collection/recovery
system (----flume path).
13 Three computer-controlled carts, with
wire-guided path.
Cart turnaround station
(up to 360° around its own axis)
Source: A tour brochure from the plant
as the washing and inspection) needed to complete the part. These programs are referred to as
process plans. Sophisticated CAD systems also are able to do on-screen tests, replacing the
early phases of prototype testing and modification.
CAD has been used to design everything from computer chips to potato chips. Frito-Lay, for
example, used CAD to design its O’Grady’s double-density, ruffled potato chip. The problem
in designing such a chip is that if it is cut improperly, it may be burned on the outside and soggy
on the inside, be too brittle (and shatter when placed in the bag), or display other characteristics
that make it unworthy for, say, a guacamole dip. However, through the use of CAD, the proper
angle and number of ruffles were determined mathematically; the O’Grady’s model passed its
stress test in the infamous Frito-Lay “crusher” and made it to your grocer’s shelf. But despite
some very loyal fans, O’Grady’s has been discontinued, presumably due to lack of sales.
CAD is now being used to custom-design swimsuits. Measurements of the wearer are fed
into the CAD program, along with the style of suit desired. Working with the customer, the
designer modifies the suit design as it appears on a human-form drawing on the computer
screen. Once the design is decided upon, the computer prints out a pattern, and the suit is cut
and sewn on the spot.
Automated manufacturing planning and control systems (MP&CS) are simply computerbased information systems that help plan, schedule, and monitor a manufacturing operation.
APPENDIX B
They obtain information from the factory floor continuously about work status, material arrivals, and so on, and they release production and purchase orders. Sophisticated manufacturing
and planning control systems include order-entry processing, shop-floor control, purchasing,
and cost accounting.
Computer-Integrated Manufacturing (CIM)
All of these automation technologies are brought together under computer-integrated manufacturing (CIM). CIM is the automated version of the manufacturing process, where the three
major manufacturing functions—product and process design, planning and control, and the
manufacturing process itself—are replaced by the automated technologies just described. Further, the traditional integration mechanisms of oral and written communication are replaced
by computer technology. Such highly automated and integrated manufacturing also goes
under the names total factory automation and the factory of the future.
All of the CIM technologies are tied together using a network and integrated database. For
instance, data integration allows CAD systems to be linked to computer-aided manufacturing
(CAM), which consists of numerical-control parts programs; and the manufacturing planning
and control system can be linked to the automated material handling systems to facilitate parts
pick list generation. Thus, in a fully integrated system, the areas of design, testing, fabrication,
assembly, inspection, and material handling are not only automated but also integrated with
each other and with the manufacturing planning and scheduling function.
E v a l u a t i o n o f T e c h n o l o g y I n v e s t m e n t s Modern technologies such as
flexible manufacturing systems or computerized order processing systems represent large
capital investments. Hence, a firm has to carefully assess its financial and strategic benefits
from a technology before acquiring it. Evaluating such investments is especially hard because
the purpose of acquiring new technologies is not just to reduce labor costs but also to increase
product quality and variety, to shorten production lead times, and to increase the flexibility
of an operation. Some of these benefits are intangible relative to labor cost reduction, so
justification becomes difficult. Further, rapid technological change renders new equipment
obsolete in just a few years, making the cost–benefit evaluation more complex.
But never assume that new automation technologies are always cost-effective. Even when
there is no uncertainty about the benefits of automation, it may not be worthwhile to adopt
it. For instance, many analysts predicted that integrated CAD/CAM systems would be the
answer to all manufacturing problems. But a number of companies investing in such systems
lost money in the process. The idea was to take a lot of skilled labor out of the process of tooling up for new or redesigned products and to speed up the process. However, it can take less
time to mill complex, low-volume parts than to program the milling machine, and programmer time is more expensive than the milling operator time. Also, it may not always be easy to
transfer all the expert knowledge and experience that a milling operator has gained over the
years into a computer program. CAD/CAM integration software has attained sufficient levels
of quality and cost-effectiveness that it is now routinely utilized even in high-variety lowvolume manufacturing environments.
B e n e f i t s o f T e c h n o l o g y I n v e s t m e n t s The typical benefits from adopting
new manufacturing technologies are both tangible and intangible. The tangible benefits can
be used in traditional modes of financial analysis such as discounted cash flow to make sound
investment decisions. Specific benefits can be summarized as follows:
Cost Reduction
Labor costs. Replacing people with robots, or enabling fewer workers to run semiautomatic equipment.
Material costs. Using existing materials more efficiently, or enabling the use of hightolerance materials.
Inventory costs. Fast changeover equipment allowing for JIT inventory management.
715
716
APPENDIX B
Quality costs. Automated inspection and reduced variation in product output.
Maintenance costs. Self-adjusting equipment.
Other Benefits
Increased product variety. Scope economies due to flexible manufacturing systems.
Improved product features. Ability to make things that could not be made by hand (e.g.,
microprocessors).
Shorter cycle times. Faster setups and changeovers.
Greater product output.
R i s k s i n A d o p t i n g N e w T e c h n o l o g i e s Although there may be many benefits
in acquiring new technologies, several types of risk accompany the acquisition of new
technologies. These risks have to be evaluated and traded off against the benefits before the
technologies are adopted. Some of these risks are described next.
Technological Risks
An early adopter of a new technology has the benefit of being ahead of the competition, but
he or she also runs the risk of acquiring an untested technology whose problems could disrupt
the firm’s operations. There is also the risk of obsolescence, especially with electronics-based
technologies where change is rapid and when the fixed cost of acquiring new technologies or
the cost of upgrades is high. Also, alternative technologies may become more cost-effective in
the future, negating the benefits of a technology today.
Operational Risks
There also could be risks in applying a new technology to a firm’s operations. Installation of
a new technology generally results in significant disruptions, at least in the short run, in the
form of plantwide reorganization, retraining, and so on. Further risks are due to the delays and
errors introduced in the production process and the uncertain and sudden demands on various
resources.
Organizational Risks
Firms may lack the organizational culture and top management commitment required to
absorb the short-term disruptions and uncertainties associated with adopting a new technology. In such organizations, there is a risk that the firm’s employees or managers may quickly
abandon the technology when there are short-term failures or they will avoid major changes
by simply automating the firm’s old, inefficient process and therefore not obtain the benefits
of the new technology.
Environmental or Market Risks
In many cases, a firm may invest in a particular technology only to discover a few years later
that changes in some environmental or market factors make the investment worthless. For
instance, in environmental issues, auto firms have been reluctant to invest in technology for
making electric cars because they are uncertain about future emission standards of state and
federal governments, the potential for decreasing emissions from gasoline-based cars, and
the potential for significant improvements in battery technology. Typical examples of market
risks are fluctuations in currency exchange rates and interest rates.
APPENDIX B
717
Concept Connections
LO B–1: Explain how the application of operations technology has affected manufacturing.
Summary
∙ Technology has played the dominant role in the productivity growth of most nations and has provided the
competitive edge to firms that have adopted it early
and implemented it successfully.
∙ Although each of the manufacturing and information technologies described here is a powerful tool
by itself and can be adopted separately, their benefits
grow exponentially when they are integrated with
each other. This is particularly the case with CIM
technologies.
•∙ With more modern technologies, the benefits are
not entirely tangible and many benefits may be realized only on a long-term basis. Thus, typical cost
accounting methods and standard financial analysis
may not adequately capture all the potential benefits
of technologies such as CIM. Hence, we must take
into account the strategic benefits in evaluating such
investments. Further, because capital costs for many
modern technologies are substantial, the various risks
associated with such investments have to be carefully
assessed.
∙ Implementing flexible manufacturing systems or complex decision support systems requires a significant
commitment for most firms. Such investments may
even be beyond the reach of small to medium-size
firms. However, as technologies continue to improve
and are adopted more widely, their costs may decline
and place them within the reach of smaller firms.
Given the complex, integrative nature of these technologies, the total commitment of top management
and all employees is critical for the successful implementation of these technologies.
Discussion Questions
1. Do robots have to be trained? Explain.
2. How does the axiom used in industrial selling “You don’t sell the product; you sell the
company” pertain to manufacturing technology?
3. List three analytical tools (other than financial analysis) covered elsewhere in the book that
can be used to evaluate technological alternatives.
4. The Belleville, Ontario, Canada, subsidiary of Atlanta-based Interface Inc., one of the
world’s largest makers of commercial flooring, credits much of its profitability to “green
manufacturing” or “eco-efficiency.” What do you believe these terms mean, eh? And how
could such practices lead to cost reduction?
5. Give two examples each of recent process and product technology innovations.
6. What is the difference between an NC machine and a machining center?
7. The major auto companies are planning to invest millions of dollars in developing new
product and process technologies required to make electric cars. Describe briefly why they
are investing in these technologies. Discuss the potential benefits and risks involved in
these investments.
A PPENDIX C
F I N A N C I A L A N A LY S I S
LO C–1
Evaluate capital
investments using the
various types of cost, risk
and expected value, and
depreciation.
In this appendix, we review the basic concepts and tools of financial analysis for OSCM.
These include the types of cost (fixed, variable, sunk, opportunity, avoidable), risk and
expected value, and depreciation (straight line, sum-of-the-years’-digits, declining balance,
double-declining-balance, and depreciation-by-use). We also discuss activity-based costing
and cost-of-capital calculations. Our focus is on capital investment decisions.
Concepts and Definitions
We begin with some basic definitions.
F i x e d C o s t s A fixed cost is any expense that remains constant regardless of the level
of output. Although no cost is truly fixed, many types of expense are virtually fixed over a
wide range of output. Examples are rent, property taxes, most types of depreciation, insurance
payments, and salaries of top management.
V a r i a b l e C o s t s Variable costs are expenses that fluctuate directly with changes in the
level of output. For example, each additional unit of sheet steel produced by USx requires
a specific amount of material and labor. The incremental cost of this additional material
and labor can be isolated and assigned to each unit of sheet steel produced. Many overhead
expenses are also variable because utility bills, maintenance expense, and so forth, vary with
the production level.
Exhibit C.1 illustrates the fixed and variable cost components of total cost. Note that total
cost increases at the same rate as variable costs because fixed costs are constant.
S u n k C o s t s Sunk costs are past expenses or investments that have no salvage value and
therefore should not be taken into account in considering investment alternatives. Sunk costs
also could be current costs that are essentially fixed such as rent on a building. For example,
suppose an ice cream manufacturing firm occupies a rented building and is considering
making sherbet in the same building. If the company enters sherbet production, its cost
accountant will assign some of the rental expense to the sherbet operation. However, the
exhibit C .1
Fixed and Variable Cost Components of Total Cost
Total cost
Variable cost
Production
cost
Fixed cost
Units of output
718
APPENDIX C
building rent remains unchanged and therefore is not a relevant expense to be considered in
making the decision. The rent is sunk; that is, it continues to exist and does not change in
amount regardless of the decision.
O p p o r t u n i t y C o s t s Opportunity cost is the benefit forgone, or advantage lost, that
results from choosing one action over the best-known alternative course of action.
Suppose a firm has $100,000 to invest and then two alternatives of comparable risk present
themselves, each requiring a $100,000 investment. Investment A will net $25,000; Investment B
will net $23,000. Investment A is clearly the better choice, with a $25,000 net return. If the decision
is made to invest in B instead of A, the opportunity cost of B is $2,000, which is the benefit forgone.
A v o i d a b l e C o s t s Avoidable costs include any expense that is not incurred if an
investment is made but that must be incurred if the investment is not made. Suppose a
company owns a metal lathe that is not in working condition but is needed for the firm’s
operations. Because the lathe must be repaired or replaced, the repair costs are avoidable if a
new lathe is purchased. Avoidable costs reduce the cost of a new investment because they are
not incurred if the investment is made. Avoidable costs are an example of how it is possible to
“save” money by spending money.
E x p e c t e d V a l u e Risk is inherent in any investment because the future can never be
predicted with absolute certainty. To deal with this uncertainty, mathematical techniques such as
expected value can help. Expected value is the expected outcome multiplied by the probability
of its occurrence. Recall that in the preceding example the expected outcome of Alternative A
was $25,000 and B, $23,000. Suppose the probability of A’s actual outcome is 80 percent while
B’s probability is 90 percent. The expected values of the alternatives are determined as follows:
Expected
​​
​​ ×
outcome
Probability that actual
​
​ ​ =
outcome
will be the ​
expected outcome
Expected
​
​
value
​
Investment A: $25,000 × 0.80 = $20, 000
​     ​​​
Investment B: $23,000 × 0.90 = $20, 700
Investment B is now seen to be the better choice, with a net advantage over A of $700.
E c o n o m i c L i f e a n d O b s o l e s c e n c e When a firm invests in an income-producing
asset, the productive life of the asset is estimated. For accounting purposes, the asset is
depreciated over this period. It is assumed that the asset will perform its function during this
time and then be considered obsolete or worn out, and replacement will be required. This
view of asset life rarely coincides with reality.
Assume that a machine expected to have a productive life of 10 years is purchased. If at any
time during the ensuing 10 years a new machine is developed that can perform the same task
more efficiently or economically, the old machine has become obsolete. Whether or not it is
“worn out” is irrelevant.
The economic life of a machine is the period over which it provides the best method for
performing its task. When a superior method is developed, the machine has become obsolete.
Thus, the stated book value of a machine can be a meaningless figure.
D e p r e c i a t i o n Depreciation is a method for allocating costs of capital equipment.
The value of any capital asset—buildings, machinery, and so forth—decreases as its useful
life is expended. Amortization and depreciation are often used interchangeably. Through
convention, however, depreciation refers to the allocation of cost due to the physical or
functional deterioration of tangible (physical) assets such as buildings or equipment, whereas
amortization refers to the allocation of cost over the useful life of intangible assets such as
patents, leases, franchises, and goodwill.
Depreciation procedures may not reflect an asset’s true value at any point in its life because
obsolescence may at any time cause a large difference between true value and book value.
719
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APPENDIX C
Also, because depreciation rates significantly affect taxes, a firm may choose a particular
method from the several alternatives with more consideration for its effect on taxes than its
ability to make the book value of an asset reflect the true resale value.
Next we describe five commonly used methods of depreciation.
Straight-Line Method
Under this method, an asset’s value is reduced in uniform annual amounts over its estimated
useful life. The general formula is
Cost − Salvage value
​Annual amount to be depreciated =_________________
​  ​
Estimated useful life
A machine costing $10,000 with an estimated salvage value of $0 and an estimated life
of 10 years would be depreciated at the rate of $1,000 per year for each of the 10 years. If its
estimated salvage value at the end of the 10 years is $1,000, the annual depreciation charge is
$10, 000 − $1, 000
_______________
​
​= $900​
10
Sum-of-the-Years’-Digits (SYD) Method
The purpose of the SYD method is to reduce the book value of an asset rapidly in early years
and at a lower rate in the later years of its life.
Suppose that the estimated useful life is five years. The numbers add up to 15: 1 + 2 + 3 +
4 + 5 = 15. Therefore, we depreciate the asset by 5 ÷ 15 after the first year, 4 ÷ 15 after the
second year, and so on, down to 1 ÷ 15 in the last year.
Declining-Balance Method
This method also achieves an accelerated depreciation. The asset’s value is decreased by reducing its book value by a constant percentage each year. The percentage rate selected is often the
one that just reduces book value to salvage value at the end of the asset’s estimated life. In any
case, the asset should never be reduced below estimated salvage value. Use of the decliningbalance method and allowable rates are controlled by Internal Revenue Service regulations. As a
simplified illustration, the preceding example is used in the next table with an arbitrarily selected
rate of 40 percent. Note that depreciation is based on full cost, not cost minus salvage value.
Year
Depreciation
Rate
Beginning
Book Value
Depreciation
Charge
Accumulated
Depreciation
Ending
Book Value
1
0.40
$17,000
$6,800
$ 6,800
$10,200
2
0.40
10,200
4,080
10,880
6,120
3
0.40
6,120
2,448
13,328
3,672
4
0.40
3,672
1,469
14,797
2,203
2,203
203
15,000
2,000
5
In the fifth year, reducing book value by 40 percent would have caused it to drop below
salvage value. Consequently, the asset was depreciated by only $203, which decreased book
value to salvage value.
Double-Declining-Balance Method
Again, for tax advantages, the double-declining-balance method offers higher depreciation early in
the life span. This method uses a percentage twice the straight line for the life span of the item but
applies this rate to the undepreciated original cost. The method is the same as the declining-balance
method, but the term double-declining balance means double the straight-line rate. Thus, equipment with a 10-year life span would have a straight-line depreciation rate of 10 percent per year and
a double-declining-balance rate (applied to the undepreciated amount) of 20 percent per year.
Depreciation-by-Use Method
The purpose of this method is to depreciate a capital investment in proportion to its use. It is
applicable, for example, to a machine that performs the same operation many times. The life
APPENDIX C
of the machine is estimated not in years but rather in the total number of operations it may reasonably be expected to perform before wearing out. Suppose that a metal-stamping press has
an estimated life of one million stamps and costs $100,000. The charge for depreciation per
stamp is then $100,000 ÷ 1,000,000, or $0.10. Assuming a $0 salvage value, the depreciation
charges are as shown in the following table.
Year
Total Yearly
Stamps
Cost
per
Stamp
Yearly
Depreciation
Charge
Accumulated
Depreciation
Ending
Book
Value
1
150,000
0.10
$15,000
$ 15,000
$85,000
2
300,000
0.10
30,000
45,000
55,000
3
200,000
0.10
20,000
65,000
35,000
4
200,000
0.10
20,000
85,000
15,000
5
100,000
0.10
10,000
95,000
5,000
6
50,000
0.10
5,000
100,000
0
The depreciation-by-use method is an attempt to gear depreciation charges to actual use and
thereby coordinate expense charges with productive output more accurately. Also, because a
machine’s resale value is related to its remaining productive life, it is hoped that book value
will approximate resale value. The danger, of course, is that technological improvements will
render the machine obsolete, in which case book value will not reflect true value.
A c t ivit y- B a s e d Cos ting
To know the costs incurred to make a certain product or deliver a service, some method of
allocating overhead costs to production activities must be applied. The traditional approach is
to allocate overhead costs to products on the basis of direct labor dollars or hours. By dividing the total estimated overhead costs by total budgeted direct labor hours, an overhead rate
can be established. The problem with this approach is that direct labor as a percentage of total
costs has fallen dramatically over the past decade. For example, the introduction of advanced
manufacturing technology and other productivity improvements has driven direct labor to as
low as 7 to 10 percent of total manufacturing costs in many industries. As a result, overhead
rates of 600 percent or even 1,000 percent are found in some highly automated plants.
This traditional accounting practice of allocating overhead to direct labor can lead to questionable investment decisions. For example, automated processes may be chosen over laborintensive processes based on a comparison of projected costs. Unfortunately, overhead does
not disappear when the equipment is installed and overall costs may actually be lower with
the labor-intensive process. It also can lead to wasted effort because an inordinate amount of
time is spent tracking direct labor hours. For example, one plant spent 65 percent of computer
costs tracking information about direct labor transactions even though direct labor accounted
for only 4 percent of total production costs.
Activity-based costing techniques have been developed to alleviate these problems by
refining the overhead allocation process to more directly reflect actual proportions of overhead consumed by the production activity. Causal factors, known as cost drivers, are identified and used as the means for allocating overhead. These factors might include machine
hours, beds occupied, computer time, flight hours, or miles driven. The accuracy of overhead
allocation, of course, depends on the selection of appropriate cost drivers.
Activity-based costing involves a two-stage allocation process, with the first stage assigning
overhead costs to cost activity pools. These pools represent activities such as performing machine
setups, issuing purchase orders, and inspecting parts. In the second stage, costs are assigned from
these pools to activities based on the number or amount of pool-related activity required in their
completion. Exhibit C.2 compares traditional cost accounting and activity-based costing.
Consider the example of activity-based costing in Exhibit C.3. Two products, A and B,
are produced using the same number of direct labor hours. The same number of direct labor
hours produces 5,000 units of Product A and 20,000 units of Product B. Applying traditional
721
722
APPENDIX C
exhibit C .2
Traditional and Activity-Based Costing
Traditional Costing
Activity-Based Costing
Total overhead
Total overhead
Labor-hour allocation
Pooled based on activities
End product cost
Cost pools
Cost-driver allocation
End product costs
exhibit C .3
Overhead Allocations by an Activity Approach
Basic Data
Activity
Machine setups
Quality inspections
Production orders
Machine-hours worked
Material receipts
Number of units produced
Events of Transactions
Traceable
Costs
$230,000
160,000
81,000
314,000
90,000
Total
Product A
Product B
5,000
8,000
600
40,000
750
25,000
3,000
5,000
200
12,000
150
5,000
2,000
3,000
400
28,000
600
20,000
$875,000
Overhead Rates by Activity
(a)
(b)
(a) ÷ (b)
Activity
Traceable
Costs
Total Events or
Transactions
Rate per Event
or Transaction
Machine setups
$230,000
5,000
$46/setups
Quality inspections
160,000
8,000
$20/inspection
Production orders
81,000
600
$135/order
314,000
40,000
$7.85/hour
90,000
750
Machine-hours worked
Material receipts
$120/receipt
Overhead Cost per Unit of Product
Product A
Product B
Events or
Transactions
Amount
Machine setups, at $46/setup
3,000
$138,000
2,000
$ 92,000
Quality inspections, at $20/inspection
5,000
100,000
3,000
60,000
200
27,000
400
54,000
12,000
94,200
28,000
219,800
18,000
600
Product orders, at $135/order
Machine-hours worked, at $7.85/hour
Material receipts, at $120/receipt
Total overhead cost assigned
150
Events or
Transactions
Amount
72,000
$377,200
$497,800
5,000
20,000
75.44
$24.89
Number of units produced
$
Note: See R. Garrison, Managerial Accounting, 12th ed. (New York: McGraw-Hill, 2007).
APPENDIX C
costing, identical overhead costs would be charged to each product. By applying activity-based
costing, traceable costs are assigned to specific activities. Because each product required a
different amount of transactions, different overhead amounts are allocated to these products
from the pools.
As stated earlier, activity-based costing overcomes the problem of cost distortion by creating a cost pool for each activity or transaction that can be identified as a cost driver, and by
assigning overhead cost to products or jobs on a basis of the number of separate activities
required for their completion. Thus, in the previous situation, the low-volume product would
be assigned the bulk of the costs for machine setup, purchase orders, and quality inspections,
thereby showing it to have high unit costs compared to the other product.
Finally, activity-based costing is sometimes referred to as transactions costing. This transactions focus gives rise to another major advantage over other costing methods: It improves the
traceability of overhead costs and thus results in more accurate unit cost data for management.
T h e E ffe cts of Ta xe s
Tax rates and the methods of applying them occasionally change. When analysts evaluate
investment proposals, tax considerations often prove to be the deciding factor because depreciation expenses directly affect taxable income and therefore profit. The ability to write off
depreciation in early years provides an added source of funds for investment. Before 1986,
firms could employ an investment tax credit, which allowed a direct reduction in tax liability.
But tax laws change, so it is crucial to stay on top of current tax laws and try to predict future
changes that may affect current investments and accounting procedures.
C h o os in g a m ong Inve s t me n t Pro p o sals
The capital investment decision has become highly rationalized, as evidenced by the variety of techniques available for its solution. In contrast to pricing or marketing decisions, the
capital investment decision can usually be made with a higher degree of confidence because
the variables affecting the decision are relatively well known and can be quantified with fair
accuracy.
Investment decisions may be grouped into six general categories:
1.
2.
3.
4.
5.
6.
Purchase of new equipment or facilities.
Replacement of existing equipment or facilities.
Make-or-buy decisions.
Lease-or-buy decisions.
Temporary shutdowns or plant abandonment decisions.
Addition or elimination of a product or product line.
Investment decisions are made with regard to the lowest acceptable rate of return on investment. As a starting point, the lowest acceptable rate of return may be considered to be the cost
of investment capital needed to underwrite the expenditure. Certainly, an investment will not
be made if it does not return at least the cost of capital.
Investments are generally ranked according to the return they yield in excess of their cost
of capital. In this way, a business with only limited investment funds can select investment
alternatives that yield the highest net returns. (Net return is the earnings an investment yields
after gross earnings have been reduced by the cost of the funds used to finance the investment.) In general, investments should not be made unless the return in funds exceeds the
marginal cost of investment capital. (Marginal cost is the incremental cost of each new acquisition of funds from outside sources.)
D e t e r m i n i n g t h e C o s t o f C a p i t a l The cost of capital is calculated from a
weighted average of debt and equity security costs. This average will vary depending on the
financing strategy employed by the company. The most common sources of financing are
723
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APPENDIX C
short-term debt, long-term debt, and equity securities. A bank loan is an example of shortterm debt. Bonds normally provide long-term debt. Finally, stock is a common form of equity
financing. In the following, we give a short example of each form of financing, and then show
how they are combined to find the weighted average cost of capital.
The cost of short-term debt depends on the interest rate on the loan and whether the loan is
discounted. Remember that interest is a tax-deductible expense for a company.
Interest paid
​Cost of short-term debt = _______________
​
​
Proceeds received
If a bank discounts a loan, interest is deducted from the face of the loan to get the proceeds.
When a compensating balance is required (that is, a percentage of the face value of the loan is
held by the bank as collateral), proceeds are also reduced. In either case, the effective or real
interest rate on the loan is higher than the face interest rate owing to the proceeds received
from the loan being less than the amount (face value) of the loan.
Example of Short-Term Debt
A company takes a $150,000, one-year, 13 percent loan. The loan is discounted, and a
10 percent compensating balance is required. The effective interest rate is computed as
follows:
13 % × $150, 000
$19, 500
_______________
​   ​= ________
​
​= 16.89%​
$115, 500
$115, 500
Proceeds received equal
Face of loan
$150,000
Less interest
(19,500)
Compensating balance (10% × $150,000)
(15,000)
Proceeds
$115,500
Notice how the effective cost of the loan is significantly greater than the stated interest rate.
Long-term debt is normally provided through the sale of corporate bonds. The real cost of
bonds is obtained by computing two types of yield: simple (face) yield and yield to maturity
(effective interest rate). The first involves an easy approximation, but the second is more accurate. The nominal interest rate equals the interest paid on the face (maturity value) of the bond
and is always stated on a per-annum basis. Bonds are generally issued in $1,000 denominations and may be sold above face value (at a premium) or below (at a discount, termed original
issue discount, or OID). A bond is sold at a discount when the interest rate is below the going
market rate. In this case, the yield will be higher than the nominal interest rate. The opposite
holds for bonds issued at a premium.
The issue price of a bond is the par (or face value) times the premium (or discount).
Nominal interest ​
Simple yield = ________________
​
Issue price of bond
Discount​​(​or premium​)​​​
___________________
​​
​  Nominal interest + ​
​
​
Years  ​
___________________________________
Yield to maturity =
​
Issue price + Maturity value
________________________
​
​
2
Example of Long-Term Debt
A company issues a $400,000, 12 percent, 10-year bond for 97 percent of face value. Yield
computations are as follows:
Nominal annual payment = 12% × $400,000
= $48,000
Bond proceeds = 97% × $400,000
= $388,000
APPENDIX C
​Bond discount = 3 % × $400, 000
= $12, 000
12 % × $400, 000 ________
$48, 000
_______________
Simple yield =
​
​ = ​
​ = 12.4%
97 % × $400, 000 $388, 000
$12, 000
$48, 000 + _______
​
​ $48, 000 + $1, 200
10
____________________
_______________
Yield to maturity =
​
​ =
​
​ = 12.5%​
$388, 000 + $400, 000
$394, 000
___________________
​
​
2
Note that because the bonds were sold at a discount, the yield exceeds the nominal interest
rate (12 percent). Bond interest is tax deductible to the corporation.
The actual cost of equity securities (stocks) comes in the form of dividends, which are not
tax deductible to the corporation.
Dividends per share
​Cost of common stock = _________________
​   ​+ Growth rate of dividends​
Value per share
Here the value per share equals the market price per share minus flotation costs (that is, the
cost of issuing securities such as brokerage fees and printing costs). It should be noted that
this valuation does not consider what the investor expects in market price appreciation. This
expectation is based on the expected growth in earnings per share and the relative risk taken
by purchasing the stock. The capital asset pricing model (CAPM) can be used to capture this
impact.
Example of the Cost of Common Stock
A company’s dividend per share is $10, net value is $70 per share, and the dividend growth
rate is 5 percent.
$10
​Cost of the stock = ____
​ ​+ 0.05 = 19.3%​
$70
To compute the weighted average cost of capital, we consider the percentage of the total
capital that is being provided by each financing alternative. We then calculate the after-tax
cost of each financing alternative. Finally, we weight these costs in proportion to their use.
Example of Calculating the Weighted Average Cost of Capital
Consider a company that shows the following figures in its financial statements:
Short-term bank loan (13%)
Bonds payable (16%)
Common stock (10%)
$1 million
$4 million
$5 million
For our example, assume that each of the percentages given represents the cost of the
source of capital. In addition to this, we need to consider the tax rate of the firm because the
interest paid on the bonds and on the short-term loan is tax deductible. Assume a corporate
tax rate of 40 percent.
Percent
After-Tax Cost
Weighted
Average Cost
Short-term bank loan
10%
13% × 60% = 7.8%
.78%
Bonds payable
40%
16% × 60% = 9.6%
3.84%
50%
10%
Common stock
Total
100%
5%
9.62%
Keep in mind that in developing this section we have made many assumptions in these
calculations. When these ideas are applied to a specific company, many of these assumptions
725
726
APPENDIX C
may change. The basic concepts, though, are the same; keep in mind that the goal is to simply
calculate the after-tax cost of the capital used by the company. We have shown the cost of
capital for the entire company, though often only the capital employed for a specific project is
used in the calculation.
I n t e r e s t R a t e E f f e c t s There are two basic ways to account for the effects of interest
accumulation. One is to compute the total amount created over the time period into the future
as the compound value. The other is to remove the interest rate effect over time by reducing all
future sums to present-day dollars, or the present value.
C o m p o u n d V a l u e o f a S i n g l e A m o u n t Albert Einstein was quoted as saying
that compound interest is the eighth wonder of the world. After reviewing this section showing
compound interest’s dramatic growth effects over a long time, you might wish to propose a
new government regulation: On the birth of a child, the parents must put, say, $1,000 into a
retirement fund for that child, available at age 65. This might reduce the pressure on Social
Security and other state and federal pension plans. Although inflation would decrease the
value significantly, there would still be a lot left over. At a 14 percent return on investment,
our $1,000 would increase to $500,000 after subtracting the $4.5 million for inflation. That is
still a 500-fold increase. (Many mutual funds today have long-term performances in excess of
14 percent per year.)
Spreadsheets and calculators make such computation easy. The OSCM at Work box titled
“Using a Spreadsheet” shows the most useful financial functions. However, many people still
refer to tables for compound values. Using Appendix I, Table I.1 (compound sum of $1), for
example, we see that the value of $1 at 10 percent interest after three years is $1.331. Multiplying this figure by $10 gives $13.31.
C o m p o u n d V a l u e o f a n A n n u i t y An annuity is the receipt of a constant sum
each year for a specified number of years. Usually an annuity is received at the end of a period
and does not earn interest during that period. Therefore, an annuity of $10 for three years
would bring in $10 at the end of the first year (allowing the $10 to earn interest if invested for
the remaining two years), $10 at the end of the second year (allowing the $10 to earn interest
for the remaining one year), and $10 at the end of the third year (with no time to earn interest).
If the annuity receipts were placed in a bank savings account at 5 percent interest, the total or
compound value of the $10 at 5 percent for the three years would be
Year
Receipt at End
of Year
Compound Interest
Factor (1 + i)n
Value at End of
Third Year
1
$10.00
×
(1 + 0.05)2
=
$11.02
2
10.00
×
1
(1 + 0.05)
=
10.50
3
10.00
×
(1 + 0.05)0
=
10.00
$31.52
The general formula for finding the compound value of an annuity is
Sn = R[(1 + i)n–1 + (1 + i)n–2 + . . . + (1 + i)1 + 1]
where
S​ n​​ = Compound value of an annuity
​
​​ =​​ Periodic receipts in dollars​ ​
R​
n = Length of the annuity in years
Applying this formula to the preceding example, we get
S​ n​​ ​= R​[​​(​1 + i​)​2​+ ​(​1 + i​)​+ 1​]​
​ ​
​
​
​ ​= $10​[​(​ ​1 + 0.05​)​2​+ (​ ​1 + 0.05​)​+ 1​]​= $31.52​
APPENDIX C
727
OSCM AT WORK
Using a Spreadsheet
We hope you are doing these calculations using a spreadsheet program. Even though the computer makes these calculations simple, it is important that you understand what
the computer is actually doing. Further, you should check
your calculations manually to make sure you have the formulas set up correctly in your spreadsheet. There are many
stories of the terrible consequences of making a wrong
decision based on a spreadsheet with errors!
For your quick reference, the following are the financial functions you will find most useful. These are from the
Microsoft Excel help screens.
PV (rate, nper, pmt)—Returns the present value of an investment. The present value is the total amount that a series
of future payments is worth now. For example, when you
borrow money, the loan amount is the present value to the
lender. Rate is the interest rate per period. For example, if
you obtain an automobile loan at a 10% annual interest rate
and make monthly payments, your interest rate per month is
10%/12, or .83%. You would enter 10%/12, or .83%, or .0083, in
the formula as the rate. Nper is the total number of payment
periods in an annuity. For example, if you get a four-year car
loan and make monthly payments, your loan has 4*12 (or 48)
periods. You would enter 48 into the formula for nper. Pmt
is the payment made each period and cannot change over
the life of the annuity. Typically, this includes principal and
interest but no other fees or taxes. For example, the monthly
payment on a $10,000, four-year car loan at 12% is $263.33.
You would enter 263.33 into the formula as pmt.
FV (rate, nper, pmt)—Returns the future value of an investment based on periodic, constant payments and a constant
interest rate. Rate is the interest rate per period. Nper is the
total number of payment periods in an annuity. Pmt is the
payment made each period; it cannot change over the life of
the annuity. Typically, pmt contains principal and interest but
no other fees or taxes.
NPV (rate, value1, value2, . . .)—Returns the net present value
of an investment based on a series of periodic cash flows and
a discount rate. The net present value of an investment is
today’s value of a series of future payments (negative values)
and income (positive values). Rate is the rate of discount over
the length of one period. Value1, value2. . ., must be equally
spaced in time and occur at the end of each period.
IRR(values)—Returns the internal rate of return for a series
of cash flows represented by the numbers in values. (Values
is defined as follows.) These cash flows do not have to be
even, as they would be for an annuity. The internal rate of
return is the interest rate received for an investment consisting of payments (negative values) and income (positive
values) that occur at regular periods. Values is an array or a
reference to cells that contain numbers for which you want
to calculate the internal rate of return. Values must contain
at least one positive value and one negative value to calculate the internal rate of return. IRR uses the order of values
to interpret the order of cash flows. Be sure to enter your
payment and income values in the sequence you want.
Source: From Microsoft Excel. Copyright © 2016 Microsoft Corporation.
In Appendix I, Table I.2 lists the compound value factor of $1 for 5 percent after three
years as 3.152. Multiplying this factor by $10 yields $31.52.
In a fashion similar to our previous retirement investment example, consider the beneficial
effects of investing $2,000 each year, just starting at the age of 21. Assume investments in
AAA-rated bonds are available today yielding 9 percent. From Table I.2 in Appendix I, after
30 years (at age 51) the investment is worth 136.3 times $2,000, or $272,600. Fourteen years
later (at age 65) this would be worth $963,044 (using a hand calculator, because the table goes
only to 30 years, and assuming the $2,000 is deposited at the end of each year)! But what
21-year-old thinks about retirement?
P r e s e n t V a l u e o f a F u t u r e S i n g l e P a y m e n t Compound values are used to
determine future value after a specific period has elapsed; present value (PV) procedures accomplish
just the reverse. They are used to determine the current value of a sum or stream of receipts expected
to be received in the future. Most investment decision techniques use present value concepts rather
than compound values. Because decisions affecting the future are made in the present, it is better
to convert future returns into their present value at the time the decision is being made. In this way,
investment alternatives are placed in better perspective in terms of current dollars.
An example makes this more apparent. If a rich uncle offers to make you a gift of $100
today or $250 after 10 years, which should you choose? You must determine whether the $250
in 10 years will be worth more than the $100 now. Suppose that you base your decision on
728
APPENDIX C
the rate of inflation in the economy and believe that inflation averages 10 percent per year. By
deflating the $250, you can compare its relative purchasing power with $100 received today.
Procedurally, this is accomplished by solving the compound formula for the present sum, P,
where V is the future amount of $250 in 10 years at 10 percent. The compound value formula is
V = P(1 + i)n
Dividing both sides by (1 + i)n gives
P = ______
​ V n​
​(​1 + i​)​ ​
​​
​
​
​ = _________
​ 250 10 ​= $96.39
​(​1 + 0.10​)​ ​
This shows that, at a 10 percent inflation rate, $250 in 10 years will be worth $96.39 today.
The rational choice, then, is to take the $100 now.
The use of tables is also standard practice in solving present value problems. With reference to Appendix I, Table I.3, the present value factor for $1 received 10 years hence is 0.386.
Multiplying this factor by $250 yields $96.50.
P r e s e n t V a l u e o f a n A n n u i t y The present value of an annuity is the value of an
annual amount to be received over a future period expressed in terms of the present. To find
the value of an annuity of $100 for three years at 10 percent, find the factor in the present value
table that applies to 10 percent in each of the three years in which the amount is received and
multiply each receipt by this factor. Then sum the resulting figures. Remember that annuities
are usually received at the end of each period.
Year
Amount Received
at End of Year
Present Value
Factor at 10%
Present
Value
1
$100
×
0.909
=
$ 90.90
2
100
×
0.826
=
82.60
3
100
×
0.751
=
75.10
Total receipts
$300
Total present value
=
$248.60
The general formula used to derive the present value of an annuity is
[
]
1 ​​
​An​​= R​​ _
​ 1 ​+ _
​ 1 ​+ . . . +​_
​(​1 + i​)​ ​(​1 + i​)​2​
​(​1 + i​)​n​
where
​ n​ ​ = Present value of an annuity of n years
A
​ ​​ =​​ Periodic receipts​
​
R​
n = Length of the annuity in years
Applying the formula to the preceding example gives
[
]
1
1
1
​ n​​ = $100​​ ​_
A
​
​+ _
​
​+ _
​
​​
2
(
)
​
1
​
+
0.10​
​
(
)
(
​
1
​
+
0.10​
​
​
​
1
​
+
0.10​)​3​ ​
​ ​
​ = $100​​(​2.487​)​= $248.70
In Appendix I, Table I.4 contains present values of an annuity for varying maturities. The
present value factor for an annuity of $1 for three years at 10 percent (from Table I.4) is 2.487.
Given that our sum is $100 rather than $1, we multiply this factor by $100 to arrive at $248.70.
When the stream of future receipts is uneven, the present value of each annual receipt must
be calculated. The present values of the receipts for all years are then summed to arrive at total
present value. This process can sometimes be tedious, but it is unavoidable.
APPENDIX C
D i s c o u n t e d C a s h F l o w The term discounted cash flow refers to the total stream of
payments that an asset will generate in the future discounted to the present time. This is simply
present value analysis that includes all flows: single payments, annuities, and all others.
M e t h od s of Ra nk ing Inv e st men t s
N e t P r e s e n t V a l u e The net present value method is commonly used in business.
With this method, decisions are based on the amount by which the present value of a projected
income stream exceeds the cost of an investment.
A firm is considering two alternative investments. The first costs $30,000 and the second,
$50,000. The expected yearly cash income streams are shown in the following table.
Cash Inflow
Year
Alternative A
Alternative B
1
$10,000
$15,000
2
10,000
15,000
3
10,000
15,000
4
10,000
15,000
5
10,000
15,000
To choose between Alternatives A and B, find which has the higher net present value.
Assume an 8 percent cost of capital.
Alternative A
3.993 (PV factor)
× $10,000
Alternative B
= $39,930
3.993 (PV factor)
× $15,000
= $59,895
Less cost of investment = 30,000
Less cost of investment = 50,000
Net present value
Net present value
= $ 9,930
= $ 9,895
Investment A is the better alternative. Its net present value exceeds that of Investment B by
$35 ($9,930 – $9,895 = $35).
P a y b a c k P e r i o d The payback method ranks investments according to the time required
for each investment to return earnings equal to the cost of the investment. The rationale is that
the sooner the investment capital can be recovered, the sooner it can be reinvested in new
revenue-producing projects. Thus, supposedly, a firm will be able to get the most benefit from
its available investment funds.
Consider two alternatives requiring a $1,000 investment each. The first will earn $200 per
year for six years; the second will earn $300 per year for the first three years and $100 per year
for the next three years.
If the first alternative is selected, the initial investment of $1,000 will be recovered at the
end of the fifth year. The income produced by the second alternative will total $1,000 after
only four years. The second alternative will permit reinvestment of the full $1,000 in new
revenue-producing projects one year sooner than the first.
Though the payback method is declining in popularity as the sole measure in investment
decisions, it is still frequently used in conjunction with other methods to indicate the time
commitment of funds. The major problems with payback are that it does not consider income
beyond the payback period and it ignores the time value of money. A method that ignores the
time value of money must be considered questionable.
I n t e r n a l R a t e o f R e t u r n The internal rate of return may be defined as the interest
rate that equates the present value of an income stream with the cost of an investment. There
is no procedure or formula that may be used directly to compute the internal rate of return—it
must be found by interpolation or iterative calculation.
729
730
APPENDIX C
Suppose we wish to find the internal rate of return for an investment costing $12,000 that will
yield a cash inflow of $4,000 per year for four years. We see that the present value factor sought is
$12, 000
_______
​
​= 3.000​
$4, 000
and we seek the interest rate that will provide this factor over a four-year period. The interest rate
must lie between 12 and 14 percent because 3.000 lies between 3.037 and 2.914 (in the fourth row
of Appendix I, Table I.4). Linear interpolation between these values, according to the equation
​(​3.037 − 3.000​)​
I = 12 + ​(​14 − 12​)____________
​
​
​(​3.037 − 2.914​)​​
​ ​
​ = 12 + 0.602 = 12.602%
gives a good approximation to the actual internal rate of return.
When the income stream is discounted at 12.6 percent, the resulting present value closely
approximates the cost of investment. Thus, the internal rate of return for this investment is
12.6 percent. The cost of capital can be compared with the internal rate of return to determine
the net rate of return on the investment. If, in this example, the cost of capital were 8 percent,
the net rate of return on the investment would be 4.6 percent.
The net present value and internal rate of return methods involve procedures that are essentially the same. They differ in that the net present value method enables investment alternatives to be compared in terms of the dollar value in excess of cost, whereas the internal rate
of return method permits comparison of rates of return on alternative investments. Moreover,
the internal rate of return method occasionally encounters problems in calculation, as multiple
rates frequently appear in the computation.
R a n k i n g I n v e s t m e n t s w i t h U n e v e n L i v e s When proposed investments
have the same life expectancy, comparison among them using the preceding methods will
give a reasonable picture of their relative value. When lives are unequal, however, there is the
question of how to relate the two different time periods. Should replacements be considered
the same as the original? Should productivity for the shorter-term unit that will be replaced
earlier be considered higher? How should the cost of future units be estimated?
No estimate dealing with investments unforeseen at the time of decision can be expected to
reflect a high degree of accuracy. Still, the problem must be dealt with, and some assumptions
must be made in order to determine a ranking.
S a m ple Pro blems: In vest men t Decisio n s
EXAMPLE C.1: An Expansion Decision
William J. Wilson Ceramic Products, Inc., leases plant facilities in which firebrick is manufactured. Because of rising demand, Wilson could increase sales by investing in new equipment
to expand output. The selling price of $10 per brick will remain unchanged if output and sales
increase. Based on engineering and cost estimates, the accounting department provides management with the following cost estimates based on an annual increased output of 100,000 bricks.
Cost of new equipment having an expected life of five years
Equipment installation cost
Expected salvage value
New operation’s share of annual lease expense
Annual increase in utility expenses
$500,000
20,000
0
40,000
40,000
Annual increase in labor costs
160,000
Annual additional cost for raw materials
400,000
The sum-of-the-years’-digits method of depreciation will be used, and taxes are paid at
a rate of 40 percent. Wilson’s policy is not to invest capital in projects earning less than a
20 percent rate of return. Should the proposed expansion be undertaken?
APPENDIX C
SOLUTION
Compute the cost of investment:
Acquisition cost of equipment
$500,000
Equipment installation costs
20,000
Total cost of investment
$520,000
Determine yearly cash flows throughout the life of the investment.
The lease expense is a sunk cost. It will be incurred whether or not the investment is
made and is therefore irrelevant to the decision and should be disregarded. Annual production
expenses to be considered are utility, labor, and raw materials. These total $600,000 per year.
Annual sales revenue is $10 × 100,000 units of output, which totals $1,000,000. Yearly
income before depreciation and taxes is thus $1,000,000 gross revenue, less $600,000
expenses, or $400,000.
Next, determine the depreciation charges to be deducted from the $500,000 income each
year using the SYD method (sum-of-years’-digits = 1 + 2 + 3 + 4 + 5 = 15).
Year
Proportion of $500,000
to Be Depreciated
Depreciation
Charge
1
5/15 × 500,000
=
$166,667
2
4/15 × 500,000
=
133,333
3
3/15 × 500,000
=
100,000
4
2/15 × 500,000
=
66,667
5
1/15 × 500,000
=
Accumulated depreciation
33,333
$500,000
Find each year’s cash flow when taxes are 40 percent. Cash flow for only the first year is
illustrated:
Earnings before depreciation and taxes
$400,000
Deduct: Taxes at 40% (40% × 400,000)
$160,000
Tax benefit of depreciation expense (0.4 × 166,667)
66,667
Cash flow (first year)
93,333
$306,667
Determine the present value of the cash flow. Because Wilson demands at least a 20 ­percent
rate of return on investments, multiply the cash flows by the 20 percent present value factor
for each year. The factor for each respective year must be used because the cash flows are not
an annuity.
Year
Present Value Factor
1
0.833
×
Cash Flow
$306,667
=
$255,454
2
0.694
×
293,333
=
203,573
3
0.579
×
280,000
=
162,120
4
0.482
×
266,667
=
128,533
5
0.402
×
253,334
=
101,840
=
$851,520
Total present value of cash flows (discounted at 20%)
Present Value
Now find whether net present value is positive or negative:
Total present value of cash flows
Total cost of investment
Net present value
$851,520
520,000
$331,520
Net present value is positive when returns are discounted at 20 percent. Wilson will earn
an amount in excess of 20 percent on the investment. The proposed expansion should be
undertaken.
731
732
APPENDIX C
EXAMPLE C.2: A Replacement Decision
For five years, Bennie’s Brewery has been using a machine that attaches labels to bottles. The
machine was purchased for $4,000 and is being depreciated over 10 years to a $0 salvage value
using straight-line depreciation. The machine can be sold now for $2,000. Bennie can buy a new
labeling machine for $6,000 that will have a useful life of five years and cut labor costs by $1,200
annually. The old machine will require a major overhaul in the next few months at an estimated cost
of $300. If purchased, the new machine will be depreciated over five years to a $500 salvage value
using the straight-line method. The company will invest in any project earning more than the 12 percent cost of capital. The tax rate is 40 percent. Should Bennie’s Brewery invest in the new machine?
SOLUTION
Determine the cost of investment:
Price of the new machine
Less: Sale of old machine
$6,000
$2,000
Avoidable overhaul costs
Effective cost of investment
300
2,300
$3,700
Determine the increase in cash flow resulting from investment in the new machine:
Yearly cost savings = $1,200
Differential depreciation
Annual depreciation on old machine:
Cost − Salvage ___________
$4, 000 − $0
_____________
​
​ =​ ​
​ =​ $400​​
Expected life
10
Annual depreciation on new machine:
Cost − Salvage _____________
$6, 000 − $500
_____________
​
​ =​ ​   ​ =​ $1,100​​
Expected life
5
Differential depreciation = $1,100 – $400 = $700
Yearly net increase in cash flow into the firm:
Cost savings
$1,200
Deduct: Taxes at 40%
$480
Add: Advantage of increase in
depreciation (0.4 × $700)
280
200
Yearly increase in cash flow
$1,000
The five-year cash flow of $1,000 per year is an annuity.
Discounted at 12 percent, the cost of capital, the present value is
3.605 × $1,000 = $3,605.
The present value of the new machine, if sold at its salvage value of $500 at the end of the
fifth year, is
0.567 × $500 = $284
Total present value of the expected cash flows is
$3,605 + $284 = $3,889
Determine whether net present value is positive:
Total present value
Cost of investment
$3,889
3,700
Net present value
$ 189
Bennie’s Brewery should make the purchase because the investment will return slightly
more than the cost of capital.
Note: The importance of depreciation has been shown in this example. The present value
of the yearly cash flow resulting from operations is
​
(​ ​Cost saving − Taxes) × (​ ​Present value factor​)​
​
​
​
​
​
​    (​ ​$1, 200 − $480​)​     ×      ​(​3.605​)​
= $2, 596
APPENDIX C
733
This figure is $1,104 less than the $3,700 cost of the investment. Only a very large depreciation advantage makes this investment worthwhile. The total present value of the advantage is
$1,009:
​(​Tax rate × Differential depreciation​)​× (PV factor​)​
​
​
​​
​
​
(0.4 × $700 )                  ×     (3.605 ) = $1, 009
EXAMPLE C.3: A Make-or-Buy Decision
Triple X Company manufactures and sells refrigerators. It makes some of the parts for the
refrigerators and purchases others. The engineering department believes it might be possible
to cut costs by manufacturing one of the parts currently being purchased for $8.25 each. The
firm uses 100,000 of these parts each year. The accounting department compiles the following list of costs based on engineering estimates:
Fixed costs will increase by $50,000.
Labor costs will increase by $125,000.
Factory overhead, currently running $500,000 per year, may be expected to increase 12
percent.
Raw materials used to make the part will cost $600,000.
Given the preceding estimates, should Triple X make the part or continue to buy it?
SOLUTION
Find the total cost incurred if the part were manufactured:
Additional fixed costs
$ 50,000
Additional labor costs
125,000
Raw materials cost
600,000
Additional overhead costs = 0.12 × $500,000
Total cost to manufacture
60,000
$835,000
Find the cost per unit to manufacture:
$835, 000
________
​
​= $8.35 per unit​
100, 000
Triple X should continue to buy the part. Manufacturing costs exceed the present cost to
purchase by $0.10 per unit.
Concept Connections
LO C–1: Evaluate capital investment decisions using the various types of cost, risk and expected
value, and depreciation.
Summary
∙ Financial analysis is essential to OSCM because many
management decisions relate to major capital investments. In this appendix, we discuss basic concepts that
are most useful in OSCM.
∙ Understanding how costs are categorized and the
most common techniques for depreciating assets
are reviewed. We use activity-based costing to
allocate common and overhead costs relative to OSCM
activities.
∙ A medium- to long-term time horizon is used when
choosing among alternative investments. When this is
the case, consideration of the time value of money by
present value analysis is useful. These decisions are
modeled using spreadsheets.
A PPENDIX D
ANSWERS TO SELECTED OBJECTIVE QUESTIONS
Chapter 1
1. Strategy, Processes, and Analytics
9. a. Receivable turnover ratio = 5.453, b. inventory
turnover ratio = 4.383, c. asset turnover ratio = 2.306
Chapter 2
1. Triple bottom line
17. Productivity (hours), Deluxe = 0.20, Limited = 0.20;
Productivity (dollars), Deluxe = 133.33, Limited =
135.71
Chapter 3
1. Testing and refinement
9. Time to market, productivity, and quality
Chapter 4
7. b. A-C-F-G-I and A-D-F-G-I, 18 weeks; c. C: one
week, D: one week, G: one week; d. Two paths: A-CF-G-I and A-D-F-G-I, 16 weeks.
12. a. A-E-G-C-D; b. 26 weeks; c. No difference in completion date.
Chapter 5
1. Capacity utilization rate = 89.1%
8. NPV – Small factory = $4.8 million; NPV – Large
factory = $2.6 million. Therefore, build small factory.
10. Capacity utilization rate = 75%. They are in the critical zone on these nights.
32 seconds and work 6.67 minutes overtime; g. 1.89
hours overtime, may be better to rebalance.
Chapter 9
1. Service package
4. Face-to-face tight specs
Chapter 10
6. a. 33.33%, b. 1/3 hour or 20 minutes, c. 1.33 students,
d. 44.44%
21. a. .2333 minutes or 14 seconds; b. 2.083 cars in
queue, 2.92 cars in the system
Chapter 11
10. Traditional method = 40 minutes, alternative method
= 51 minutes. Traditional method is best.
12. a. The market can only be served at 3 gal/hour and
in 50 hours the bathtub will overflow; b. The average
amount being serviced is 2.5 gal/hour, so that is the
output rate.
Chapter 12
6. DPMO = 15,333; this is not very good.
11. Opportunity flow diagram
Chapter 6
5. 4,710 hours
7. Learning rate – Labor = 80%, Learning rate – Parts =
90%; Labor = 11,556 hours, Parts = $330,876
Chapter 13
1. a. Cost when not inspecting = $20/hr, cost to inspect
= $9/hr, therefore inspect; b. $0.18 each; c. $0.22 per
unit.
6. a. .333, b. No, the machine is not capable of high
enough quality.
9. UCL = 1014.965, LCL = 983.235 for X-bar chart;
UCL = 49.552, LCL = 0.00 for the R-chart.
Chapter 7
9. Break-even = 7,500 units
16. 80 units/hour
Chapter 14
10. Five kanban card sets
14. Five kanban card sets
Chapter 8
5. b. 120 seconds/unit; c. station 1 (AD), station 2 (BC),
station 3 (EF), station 4 (GH); d. 87.5%
10. a. 33.6 seconds/unit; b. 3.51 → 4 workstations; d. station 1 (AB), station 2 (DF), station 3 (C), station 4
(EF), station 5 (H); e. 70.2%; f. Reduce cycle time to
Chapter 15
9. Total cost $1,056.770; b. Should consider closing the
Philadelphia plant because we are using very little of
the capacity from that plant.
10. Cx = 373.8, Cy = 356.9
734
Chapter 16
11. Buy NPV = $143,226.27, make NPV = $84,442.11,
we should accept the bid.
16. Inventory turn = 148.6, weeks of supply = .350 (1/3
of a week’s supply on hand)
Chapter 17
5. Manufacturing and logistics
11. 9.61 days
Chapter 18
3. 3rd most recent = 1,000, 2nd most recent = 1,175,
most recent = 975
6. a. February 84, March 86, April 90, May 88, June 84;
b. MAD = 15
21. a. MAD = 90, TS = –1.67; b. TS acceptable for now,
but is trending downward.
Chapter 19
7. Total cost = $416,600
10. Total cost = $413,750
APPENDIX D
7. Select car C first, then A and B tie for second.
9. Critical ratio schedule: 5, 3, 2, 4, 1; Earliest due date
schedule: 2, 5, 3, 4, 1; Shortest processing time: 2, 1,
4, 3, 5
Chapter 23
6. Case I:X used = 933.3 hours, Y used
= 700 hours
Case II:X used = 933.3 hours, Y used
= 700 hours
Case III:X used = 933.3 hours, Y used
= 700 hours
Case IV:X used = 933.3 hours, Y used
= 700 hours
With no restrictions.
Case I:
No problem
Case II:
Excess WIP
Case III:
Excess spare parts
Case IV:
Excess finished goods
17. a. Machine B is the constraint; b. All 100 of M, as
many N as possible; c. $600 (100 M and 30 N)
Chapter 20
4. Purchase 268 boxes of lettuce.
14. q = 713
17. a. Q = 1,225, R = 824; b. q = 390 – I
Chapter 24
2. Staff flows
6. Clinical dashboard
Chapter 21
11. a.
Chapter 25
7. Balanced scorecard
11. Codification of reengineering
Level
Z
A(2)
C(3)
0
B(4)
1
D(4)
2
E(2)
3
21. Least total cost order 180 to cover periods 4 through
8. Least unit cost is tied for ordering 180 for periods 4
through 8, or order 220 units to cover 4 through 9.
Chapter 22
5. Run the jobs in the following order: 103, 105, 101,
102, 104. Mean flow time = 16.2 days.
735
Appendix A
2. Optimal combination is B = 10, A = 15, and Z = 70.
4. a. 600A + 900B < = 3, 600
​ 600A + 900B > = 1, 800
​ ​ 200A + 700B
< = 1, 400
​
​
​
​ ​
​ 400A + 100B > = 400
​ A < =2
​ Minimize .75A + .15B
b. A = 0.54
​ ​ ​ B = 1.85​
​ ​
​ Obj = 0.68
A PPENDIX E
P R E S E N T VA L U E TA B L E
exhibit E.1
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
1%
.990
.980
.971
.961
.951
.942
.933
.923
.914
.905
.896
.887
.879
.870
.861
.853
.844
.836
.828
.820
.780
.742
16%
.862
.743
.641
.552
.476
.410
.354
.305
.263
.227
.195
.168
.145
.125
.108
.093
.080
.069
.060
.051
.024
.012
2%
.980
.961
.942
.924
.906
.888
.871
.853
.837
.820
.804
.788
.773
.758
.743
.728
.714
.700
.686
.673
.610
.552
18%
.847
.718
.609
.516
.437
.370
.314
.266
.226
.191
.162
.137
.116
.099
.084
.071
.060
.051
.043
.037
.016
.007
Costs of Four Production Plans
3%
.971
.943
.915
.889
.863
.838
.813
.789
.766
.744
.722
.701
.681
.661
.642
.623
.605
.587
.570
.554
.478
.412
20%
.833
.694
.579
.482
.402
.335
.279
.233
.194
.162
.135
.112
.093
.078
.065
.054
.045
.038
.031
.026
.010
.004
4%
.962
.925
.889
.855
.822
.790
.760
.731
.703
.676
.650
.625
.601
.577
.555
.534
.513
.494
.475
.456
.375
.308
24%
.806
.650
.524
.423
.341
.275
.222
.179
.144
.116
.094
.076
.061
.049
.040
.032
.026
.021
.017
.014
.005
.002
5%
.952
.907
.864
.823
.784
.746
.711
.677
.645
.614
.585
.557
.530
.505
.481
.458
.436
.416
.396
.377
.295
.231
28%
.781
.610
.477
.373
.291
.227
.178
.139
.108
.085
.066
.052
.040
.032
.025
.019
.015
.012
.009
.007
.002
.001
6%
.943
.890
.840
.792
.747
.705
.665
.627
.592
.558
.527
.497
.469
.442
.417
.394
.371
.350
.331
.312
.233
.174
32%
.758
.574
.435
.329
.250
.189
.143
.108
.082
.062
.047
.036
.027
.021
.016
.012
.009
.007
.005
.004
.001
.000
7%
.935
.873
.816
.763
.713
.666
.623
.582
.544
.508
.475
.444
.415
.388
.362
.339
.317
.296
.276
.258
.184
.131
36%
.735
.541
.398
.292
.215
.158
.116
.085
.063
.046
.034
.025
.018
.014
.010
.007
.005
.004
.003
.002
.000
.000
8%
.926
.857
.794
.735
.681
.630
.583
.540
.500
.463
.429
.397
.368
.340
.315
.292
.270
.250
.232
.215
.146
.099
40%
.714
.510
.364
.260
.186
.133
.095
.068
.048
.035
.025
.018
.013
.009
.006
.005
.003
.002
.002
.001
.000
Using Microsoft Excel, these are calculated with the equation: (1 + interest)–years.
736
9%
.917
.842
.772
.708
.650
.596
.547
.502
.460
.422
.388
.356
.326
.299
.275
.252
.231
.212
.194
.178
.116
.075
50%
.667
.444
.296
.198
.132
.088
.059
.039
.026
.017
.012
.008
.005
.003
.002
.002
.001
.001
.000
.000
10%
.909
.826
.751
.683
.621
.564
.513
.467
.424
.386
.350
.319
.290
.263
.239
.218
.198
.180
.164
.149
.092
.057
60%
.625
.391
.244
.153
.095
.060
.037
.023
.015
.009
.006
.004
.002
.001
.001
.001
.000
.000
.000
.000
12%
.893
.797
.712
.636
.567
.507
.452
.404
.361
.322
.287
.257
.229
.205
.183
.163
.146
.130
.116
.104
.059
.033
70%
.588
.346
.204
.120
.070
.041
.024
.014
.008
.005
.003
.002
.001
.001
.000
.000
.000
.000
14%
.877
.769
.675
.592
.519
.456
.400
.351
.308
.270
.237
.208
.182
.160
.140
.123
.108
.095
.083
.073
.038
.020
80%
.556
.309
.171
.095
.053
.029
.016
.009
.005
.003
.002
.001
.001
.000
.000
.000
15%
.870
.756
.658
.572
.497
.432
.376
.327
.284
.247
.215
.187
.163
.141
.123
.107
.093
.081
.070
.061
.030
.015
90%
.526
.277
.146
.077
.040
.021
.011
.006
.003
.002
.001
.001
.000
.000
.000
A PPENDIX F
N E G AT I V E E X P O N E N T I A L D I S T R I B U T I O N : VA LU E S O F E – X
e –x
1.0
.5
.5
X
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.50
e–X
(VALUE)
1.00000
.99005
.98020
.97045
.96079
.95123
.94176
.93239
.92312
.91393
.90484
.89583
.88692
.87809
.86936
.86071
.87514
.84366
.83527
.82696
.81873
.81058
.80252
.79453
.78663
.77880
.77105
.76338
.75578
.74826
.74082
.73345
.72615
.71892
.71177
.70469
.69768
.69073
.68386
.67706
.67032
.66365
.65705
.65051
.64404
.63763
.63128
.62500
.61878
.61263
.60653
X
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.70
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
e–X
(VALUE)
.60050
.59452
.58860
.58275
.57695
.57121
.56553
.55990
.55433
.54881
.54335
.53794
.53259
.52729
.52205
.51685
.51171
.50662
.50158
.49659
.49164
.48675
.48191
.47711
.47237
.46767
.46301
.45841
.45384
.44933
.44486
.44043
.43605
.43171
.42741
.42316
.41895
.41478
.41066
.40657
.40252
.39852
.39455
.39063
.38674
.38289
.37908
.37531
.37158
.36788
1.0 1.5
x
X
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.30
1.31
1.32
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
1.50
e–X
(VALUE)
.36422
.36060
.35701
.35345
.34994
.34646
.34301
.33960
.33622
.33287
.32956
.32628
.32303
.31982
.31664
.31349
.31037
.30728
.30422
.30119
.29820
.29523
.29229
.28938
.28650
.28365
.28083
.27804
.27527
.27253
.26982
.26714
.26448
.26185
.25924
.25666
.25411
.25158
.24908
.24660
.24414
.24171
.23931
.23693
.23457
.23224
.22993
.22764
.22537
.22313
X
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.70
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.80
1.81
1.82
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.90
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
2.00
e–X
(VALUE)
.22091
.21871
.21654
.21438
.21225
.21014
.20805
.20598
.20393
.20190
.19989
.19790
.19593
.19398
.19205
.19014
.18825
.18637
.18452
.18268
.18087
.17907
.17728
.17552
.17377
.17204
.17033
.16864
.16696
.16530
.16365
.16203
.16041
.15882
.15724
.15567
.15412
.15259
.15107
.14957
.14808
.14661
.14515
.14370
.14227
.14086
.13946
.13807
.13670
.13534
Using Microsoft Excel, these values are calculated with the equation: 1 − EXPONDIST(x, 1, TRUE).
737
A PPENDIX G
A R E A S O F T H E C U M U L AT I V E S TA N DA R D N O R M A L
DISTRIBUTION
z
An entry in the table is the proportion under the curve cumulated from the negative tail.
z
−4.00
−3.95
−3.90
−3.85
−3.80
−3.75
−3.70
−3.65
−3.60
−3.55
−3.50
−3.45
−3.40
−3.35
−3.30
−3.25
−3.20
−3.15
−3.10
−3.05
−3.00
−2.95
−2.90
−2.85
−2.80
−2.75
−2.70
−2.65
−2.60
−2.55
−2.50
−2.45
−2.40
−2.35
−2.30
−2.25
−2.20
−2.15
−2.10
−2.05
−2.00
G(z)
0.00003
0.00004
0.00005
0.00006
0.00007
0.00009
0.00011
0.00013
0.00016
0.00019
0.00023
0.00028
0.00034
0.00040
0.00048
0.00058
0.00069
0.00082
0.00097
0.00114
0.00135
0.00159
0.00187
0.00219
0.00256
0.00298
0.00347
0.00402
0.00466
0.00539
0.00621
0.00714
0.00820
0.00939
0.01072
0.01222
0.01390
0.01578
0.01786
0.02018
0.02275
z
−1.95
−1.90
−1.85
−1.80
−1.75
−1.70
−1.65
−1.60
−1.55
−1.50
−1.45
−1.40
−1.35
−1.30
−1.25
−1.20
−1.15
−1.10
−1.05
−1.00
−0.95
−0.90
−0.85
−0.80
−0.75
−0.70
−0.65
−0.60
−0.55
−0.50
−0.45
−0.40
−0.35
−0.30
−0.25
−0.20
−0.15
−0.10
−0.05
0.00
0.05
G(z)
0.02559
0.02872
0.03216
0.03593
0.04006
0.04457
0.04947
0.05480
0.06057
0.06681
0.07353
0.08076
0.08851
0.09680
0.10565
0.11507
0.12507
0.13567
0.14686
0.15866
0.17106
0.18406
0.19766
0.21186
0.22663
0.24196
0.25785
0.27425
0.29116
0.30854
0.32636
0.34458
0.36317
0.38209
0.40129
0.42074
0.44038
0.46017
0.48006
0.50000
0.51994
z
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
G(z)
0.53983
0.55962
0.57926
0.59871
0.61791
0.63683
0.65542
0.67364
0.69146
0.70884
0.72575
0.74215
0.75804
0.77337
0.78814
0.80234
0.81594
0.82894
0.84134
0.85314
0.86433
0.87493
0.88493
0.89435
0.90320
0.91149
0.91924
0.92647
0.93319
0.93943
0.94520
0.95053
0.95543
0.95994
0.96407
0.96784
0.97128
0.97441
0.97725
0.97982
0.98214
Using Microsoft Excel, these probabilities are generated with the NORMSDIST(z) function.
738
z
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
3.85
3.90
3.95
4.00
G(z)
0.98422
0.98610
0.98778
0.98928
0.99061
0.99180
0.99286
0.99379
0.99461
0.99534
0.99598
0.99653
0.99702
0.99744
0.99781
0.99813
0.99841
0.99865
0.99886
0.99903
0.99918
0.99931
0.99942
0.99952
0.99960
0.99966
0.99972
0.99977
0.99981
0.99984
0.99987
0.99989
0.99991
0.99993
0.99994
0.99995
0.99996
0.99997
A PPENDIX H
U N I F O R M LY D I S T R I B U T E D R A N D O M D I G I T S
56970
83125
55503
47019
84828
08021
36458
05752
26768
42613
95457
95276
66954
17457
03704
21538
57178
31048
69799
90595
33570
15340
64079
63491
92003
52360
74622
04157
86003
41208
06433
39298
89884
61512
99653
95913
55804
35334
57729
86648
30574
81307
02410
18969
87863
08397
28520
44285
86299
84842
10799
85077
21383
06683
61152
31331
28285
96045
02513
72456
12176
67524
53574
44151
23322
16997
16730
40058
83300
65017
34761
82760
07733
84886
76568
46658
12142
50070
60070
80187
80674
47829
59651
32155
47635
11085
44004
82410
88646
89317
06039
13114
96385
87444
80514
10538
45247
09452
22510
05748
52098
60490
02464
33203
79526
79227
30424
36847
58454
43030
65482
63564
64776
14113
83214
33210
08310
94953
16498
59231
08039
57477
36512
67118
41034
66511
68355
61343
66241
20351
24520
72648
67533
51906
12506
13772
13122
91601
76487
63677
07967
83580
79067
52233
66860
15438
58729
15867
33571
90894
04184
44369
26141
29603
29554
05748
98420
87729
56958
58085
25596
95958
92345
02462
59337
60337
70348
55866
80733
17772
78784
13898
56186
62063
28260
04172
65635
64315
32836
09630
18222
37414
68123
61662
88535
76638
44115
40617
11622
70119
32422
79974
54939
62319
62297
62311
10854
70418
23309
61658
54967
66130
68779
54553
84580
51276
72925
81679
20575
06766
02678
39750
95110
02798
01695
27976
11317
96283
96422
67831
09977
48431
99098
74958
79708
73085
21828
70836
27573
84668
10610
75755
17730
64430
36553
48423
01601
72876
96297
94739
76791
45929
21410
08598
80198
72844
99058
57012
57040
15001
72938
72936
66388
25971
37859
57143
40729
59126
76746
60227
54592
64379
59448
54977
60666
70661
71623
40620
58078
33317
29398
72936
48850
20946
00770
11795
39539
82857
11479
42486
05794
04717
95862
16688
23757
25018
50541
33967
24160
25875
30725
85113
86980
09066
19347
60203
18260
72122
29285
94005
50834
69848
75242
69573
28504
31926
22337
59437
40878
96414
63607
46059
77249
48340
97410
08250
55510
52087
99643
00520
93896
78160
72527
28147
88643
52594
18988
35335
94114
71303
37515
29899
08034
37275
34209
99041
00147
73830
09903
38829
53711
72268
91772
95288
73234
46412
38765
36634
67870
36308
23777
59973
82690
83854
61980
00915
48293
33225
06846
32671
82096
51666
54044
66738
55064
69509
64750
80817
39847
90401
78227
87240
08486
39338
21188
13287
53609
87900
81641
19512
48619
78817
19473
51262
55803
77529
77685
15405
14047
68377
93385
09858
93307
04794
86265
65943
90038
97283
21913
41161
08392
08144
74099
24715
34997
45821
86847
31280
32828
45587
21913
10433
67942
60184
17427
60264
87759
74533
96884
41700
90110
52710
10951
32109
01850
82531
04001
36194
00496
50277
62866
03509
63971
11569
96275
81360
58788
96554
22917
43918
13421
52104
34116
01534
49096
79232
94209
95943
72958
37341
739
A PPENDIX I
I N T E R E S T TA B L E S
exhibit I.1
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
Compound Sum of $1
1%
1.010
1.020
1.030
1.041
1.051
1.062
1.072
1.083
1.094
1.105
1.116
1.127
1.138
1.149
1.161
1.173
1.184
1.196
1.208
1.220
1.282
1.348
10%
2%
1.020
1.040
1.061
1.082
1.104
1.126
1.149
1.172
1.195
1.219
1.243
1.268
1.294
1.319
1.346
1.373
1.400
1.428
1.457
1.486
1.641
1.811
12%
3%
1.030
1.061
1.093
1.126
1.159
1.194
1.230
1.267
1.305
1.344
1.384
1.426
1.469
1.513
1.558
1.605
1.653
1.702
1.754
1.806
2.094
2.427
14%
4%
1.040
1.082
1.125
1.170
1.217
1.265
1.316
1.369
1.423
1.480
1.539
1.601
1.665
1.732
1.801
1.873
1.948
2.026
2.107
2.191
2.666
3.243
15%
5%
1.050
1.102
1.158
1.216
1.276
1.340
1.407
1.477
1.551
1.629
1.710
1.796
1.886
1.980
2.079
2.183
2.292
2.407
2.527
2.653
3.386
4.322
16%
6%
1.060
1.124
1.191
1.262
1.338
1.419
1.504
1.594
1.689
1.791
1.898
2.012
2.133
2.261
2.397
2.540
2.693
2.854
3.026
3.207
4.292
5.743
18%
7%
1.070
1.145
1.225
1.311
1.403
1.501
1.606
1.718
1.838
1.967
2.105
2.252
2.410
2.579
2.759
2.952
3.159
3.380
3.617
3.870
5.427
7.612
20%
8%
1.080
1.166
1.260
1.360
1.469
1.587
1.714
1.851
1.999
2.159
2.332
2.518
2.720
2.937
3.172
3.426
3.700
3.996
4.316
4.661
6.848
10.063
24%
9%
1.090
1.188
1.295
1.412
1.539
1.677
1.828
1.993
2.172
2.367
2.580
2.813
3.066
3.342
3.642
3.970
4.328
4.717
5.142
5.604
8.623
13.268
28%
1.100
1.210
1.331
1.464
1.611
1.772
1.949
2.144
2.358
2.594
2.853
3.138
3.452
3.797
4.177
4.595
5.054
5.560
6.116
6.728
10.835
17.449
1.120
1.254
1.405
1.574
1.762
1.974
2.211
2.476
2.773
3.106
3.479
3.896
4.363
4.887
5.474
6.130
6.866
7.690
8.613
9.646
17.000
29.960
1.140
1.300
1.482
1.689
1.925
2.195
2.502
2.853
3.252
3.707
4.226
4.818
5.492
6.261
7.138
8.137
9.276
10.575
12.056
13.743
26.462
50.950
1.150
1.322
1.521
1.749
2.011
2.313
2.660
3.059
3.518
4.046
4.652
5.350
6.153
7.076
8.137
9.358
10.761
12.375
14.232
16.367
32.919
66.212
1.160
1.346
1.561
1.811
2.100
2.436
2.826
3.278
3.803
4.411
5.117
5.936
6.886
7.988
9.266
10.748
12.468
14.463
16.777
19.461
40.874
85.850
1.180
1.392
1.643
1.939
2.288
2.700
3.185
3.759
4.435
5.234
6.176
7.288
8.599
10.147
11.974
14.129
16.672
19.673
23.214
27.393
62.669
143.371
1.200
1.440
1.728
2.074
2.488
2.986
3.583
4.300
5.160
6.192
7.430
8.916
10.699
12.839
15.407
18.488
22.186
26.623
31.948
38.338
95.396
237.376
1.240
1.538
1.907
2.364
2.932
3.635
4.508
5.590
6.931
8.594
10.657
13.216
16.386
20.319
25.196
31.243
38.741
48.039
59.568
73.864
216.542
634.820
1.280
1.638
2.067
2.684
3.436
4.398
5.629
7.206
9.223
11.806
15.112
19.343
24.759
31.691
40.565
51.923
66.461
85.071
108.89
139.38
478.90
1645.5
Using Microsoft Excel, these are calculated with the equation: (1 + interest)years.
740
exhibit I.2
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
1%
1.000
2.010
2.030
4.060
5.101
6.152
7.214
8.286
9.369
10.462
11.567
12.683
13.809
14.947
16.097
17.258
18.430
19.615
20.811
22.019
28.243
34.785
741
APPENDIX I
Sum of an Annuity of $1 for N Years
2%
1.000
2.020
3.060
4.122
5.204
6.308
7.434
8.583
9.755
10.950
12.169
13.412
14.680
15.974
17.293
18.639
20.012
21.412
22.841
24.297
32.030
40.568
3%
1.000
2.030
3.019
4.184
5.309
6.468
7.662
8.892
10.159
11.464
12.808
14.192
15.618
17.086
18.599
20.157
21.762
23.414
25.117
26.870
36.459
47.575
4%
1.000
2.040
3.122
4.246
5.416
6.633
7.898
9.214
10.583
12.006
13.486
15.026
16.627
18.292
20.024
21.825
23.698
25.645
27.671
29.778
41.646
56.085
5%
1.000
2.050
3.152
4.310
5.526
6.802
8.142
9.549
11.027
12.578
14.207
15.917
17.713
19.599
21.579
23.657
25.840
28.132
30.539
33.066
47.727
66.439
6%
1.000
2.060
3.184
4.375
5.637
6.975
8.394
9.897
11.491
13.181
14.972
16.870
18.882
21.051
23.276
25.673
28.213
30.906
33.760
36.786
54.865
79.058
7%
1.000
2.070
3.215
4.440
5.751
7.153
8.654
10.260
11.978
13.816
15.784
17.888
20.141
22.550
25.129
27.888
30.840
33.999
37.379
40.995
63.249
94.461
8%
1.000
2.080
3.246
4.506
5.867
7.336
8.923
10.637
12.488
14.487
16.645
18.977
21.495
24.215
27.152
30.324
33.750
37.450
41.446
45.762
73.106
113.283
Year
9%
10%
12%
14%
16%
18%
20%
24%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
1.000
2.090
3.278
4.573
5.985
7.523
9.200
11.028
13.021
15.193
17.560
20.141
22.953
26.019
29.361
33.003
36.974
41.301
46.018
51.160
84.701
136.308
1.000
2.100
3.310
4.641
6.105
7.716
9.487
11.436
13.579
15.937
18.531
21.384
24.523
27.975
31.772
35.950
40.545
45.599
51.159
57.275
93.347
164.494
1.000
2.120
3.374
4.770
6.353
8.115
10.089
12.300
14.776
17.549
20.655
24.133
28.029
32.393
37.280
42.753
48.884
55.750
63.440
72.052
133.334
241.333
1.000
2.140
3.440
4.921
6.610
8.536
10.730
13.233
16.085
19.337
23.044
27.271
32.089
37.581
43.842
50.980
59.118
68.394
78.969
91.025
181.871
356.787
1.000
2.160
3.506
5.066
6.877
8.977
11.414
14.240
17.518
21.321
25.733
30.850
36.786
43.672
51.660
60.925
71.673
84.141
98.603
115.380
249.214
530.312
1.000
2.180
3.572
5.215
7.154
9.442
12.142
15.327
19.086
23.521
28.755
34.931
42.219
50.818
60.965
72.939
87.068
103.740
123.414
146.628
342.603
790.948
1.000
2.200
3.640
5.368
7.442
9.930
12.916
16.499
20.799
25.959
32.150
39.580
48.497
59.196
72.035
87.442
105.931
128.117
154.740
186.688
471.981
1181.882
1.000
2.240
3.778
5.684
8.048
10.980
14.615
19.123
24.712
31.643
40.238
50.985
64.110
80.496
100.815
126.011
157.253
195.994
244.033
303.601
898.092
2640.916
Using Microsoft Excel, these are calculated with the function: FV(interest, years, −1).
742
APPENDIX I
Present Value of $1
exhibit I.3
Year
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
15%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
.990
.980
.971
.961
.951
.942
.933
.923
.914
.905
.896
.887
.879
.870
.861
.853
.844
.836
.828
.820
.780
.742
.980
.961
.942
.924
.906
.888
.871
.853
.837
.820
.804
.788
.773
.758
.743
.728
.714
.700
.686
.673
.610
.552
.971
.943
.915
.889
.863
.838
.813
.789
.766
.744
.722
.701
.681
.661
.642
.623
.605
.587
.570
.554
.478
.412
.962
.925
.889
.855
.822
.790
.760
.731
.703
.676
.650
.625
.601
.577
.555
.534
.513
.494
.475
.456
.375
.308
.952
.907
.864
.823
.784
.746
.711
.677
.645
.614
.585
.557
.530
.505
.481
.458
.436
.416
.396
.377
.295
.231
.943
.890
.840
.792
.747
.705
.665
.627
.592
.558
.527
.497
.469
.442
.417
.394
.371
.350
.331
.312
.233
.174
.935
.873
.816
.763
.713
.666
.623
.582
.544
.508
.475
.444
.415
.388
.362
.339
.317
.296
.276
.258
.184
.131
.926
.857
.794
.735
.681
.630
.583
.540
.500
.463
.429
.397
.368
.340
.315
.292
.270
.250
.232
.215
.146
.099
.917
.842
.772
.708
.650
.596
.547
.502
.460
.422
.388
.356
.326
.299
.275
.252
.231
.212
.194
.178
.116
.075
.909
.826
.751
.683
.621
.564
.513
.467
.424
.386
.350
.319
.290
.263
.239
.218
.198
.180
.164
.149
.092
.057
.893
.797
.712
.636
.567
.507
.452
.404
.361
.322
.287
.257
.229
.205
.183
.163
.146
.130
.116
.104
.059
.033
.877
.769
.675
.592
.519
.456
.400
.351
.308
.270
.237
.208
.182
.160
.140
.123
.108
.095
.083
.073
.038
.020
.870
.756
.658
.572
.497
.432
.376
.327
.284
.247
.215
.187
.163
.141
.123
.107
.093
.081
.070
.061
.030
.015
Year
16%
18%
20%
24%
28%
32%
36%
40%
50%
60%
70%
80%
90%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
.862
.743
.641
.552
.476
.410
.354
.305
.263
.227
.195
.168
.145
.125
.108
.093
.080
.069
.060
.051
.024
.012
.847
.718
.609
.516
.437
.370
.314
.266
.226
.191
.162
.137
.116
.099
.084
.071
.060
.051
.043
.037
.016
.007
.833
.694
.579
.482
.402
.335
.279
.233
.194
.162
.135
.112
.093
.078
.065
.054
.045
.038
.031
.026
.010
.004
.806
.650
.524
.423
.341
.275
.222
.179
.144
.116
.094
.076
.061
.049
.040
.032
.026
.021
.017
.014
.005
.002
.781
.610
.477
.373
.291
.227
.178
.139
.108
.085
.066
.052
.040
.032
.025
.019
.015
.012
.009
.007
.002
.001
.758
.574
.435
.329
.250
.189
.143
.108
.082
.062
.047
.036
.027
.021
.016
.012
.009
.007
.005
.004
.001
.000
.735
.541
.398
.292
.215
.158
.116
.085
.063
.046
.034
.025
.018
.014
.010
.007
.005
.004
.003
.002
.000
.000
.714
.510
.364
.260
.186
.133
.095
.068
.048
.035
.025
.018
.013
.009
.006
.005
.003
.002
.002
.001
.000
.667
.444
.296
.198
.132
.088
.059
.039
.026
.017
.012
.008
.005
.003
.002
.002
.001
.001
.000
.000
.625
.391
.244
.153
.095
.060
.037
.023
.015
.009
.006
.004
.002
.001
.001
.001
.000
.000
.000
.000
.588
.346
.204
.120
.070
.041
.024
.014
.008
.005
.003
.002
.001
.001
.000
.000
.000
.000
.556
.309
.171
.095
.053
.029
.016
.009
.005
.003
.002
.001
.001
.000
.000
.000
.526
.277
.146
.077
.040
.021
.011
.006
.003
.002
.001
.001
.000
.000
.000
Using Microsoft Excel, these are calculated with the equation: (1 + interest)–years.
Present Value of an Annuity of $1
exhibit I.4
Year
1%
743
APPENDIX I
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
0.990
0.980
0.971
0.962
0.952
0.943
0.935
0.926
0.917
0.909
2
1.970
1.942
1.913
1.886
1.859
1.833
1.808
1.783
1.759
1.736
3
2.941
2.884
2.829
2.775
2.723
2.673
2.624
2.577
2.531
2.487
4
3.902
3.808
3.717
3.630
3.546
3.465
3.387
3.312
3.240
3.170
5
4.853
4.713
4.580
4.452
4.329
4.212
4.100
3.993
3.890
3.791
6
5.795
5.601
5.417
5.242
5.076
4.917
4.766
4.623
4.486
4.355
7
6.728
6.472
6.230
6.002
5.786
5.582
5.389
5.206
5.033
4.868
8
7.652
7.325
7.020
6.733
6.463
6.210
6.971
5.747
5.535
5.335
9
8.566
8.162
7.786
7.435
7.108
6.802
6.515
6.247
5.985
5.759
10
9.471
8.983
8.530
8.111
7.722
7.360
7.024
6.710
6.418
6.145
11
10.368
9.787
9.253
8.760
8.306
7.887
7.449
7.139
6.805
6.495
12
11.255
10.575
9.954
9.385
8.863
8.384
7.943
7.536
7.161
6.814
13
12.134
11.348
10.635
9.986
9.394
8.853
8.358
7.904
7.487
7.103
14
13.004
12.106
11.296
10.563
9.899
9.295
8.745
8.244
7.786
7.367
15
13.865
12.849
11.938
11.118
10.380
9.712
9.108
8.559
8.060
7.606
16
14.718
13.578
12.561
11.652
10.838
10.106
9.447
8.851
8.312
7.824
17
15.562
14.292
13.166
12.166
11.274
10.477
9.763
9.122
8.544
8.022
18
16.398
14.992
13.754
12.659
11.690
10.828
10.059
9.372
8.756
8.201
19
17.226
15.678
14.324
13.134
12.085
11.158
10.336
9.604
8.950
8.365
20
18.046
16.351
14.877
13.590
12.462
11.470
10.594
9.818
9.128
8.514
25
22.023
19.523
17.413
15.622
14.094
12.783
11.654
10.675
9.823
9.077
30
25.808
22.397
19.600
17.292
15.373
13.765
12.409
11.258
10.274
9.427
Year
12%
14%
16%
18%
20%
24%
28%
32%
36%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
0.893
1.690
2.402
3.037
3.605
4.111
4.564
4.968
5.328
5.650
5.988
6.194
6.424
6.628
6.811
6.974
7.120
7.250
7.366
7.469
7.843
8.055
0.877
1.647
2.322
2.914
3.433
3.889
4.288
4.639
4.946
5.216
5.453
5.660
5.842
6.002
6.142
6.265
6.373
6.467
6.550
6.623
6.873
7.003
0.862
1.605
2.246
2.798
3.274
3.685
4.039
4.344
4.607
4.833
5.029
5.197
5.342
5.468
5.575
5.669
5.749
5.818
5.877
5.929
6.097
6.177
0.847
1.566
2.174
2.690
3.127
3.498
3.812
4.078
4.303
4.494
4.656
4.793
4.910
5.008
5.092
5.162
5.222
5.273
5.316
5.353
5.467
5.517
0.833
1.528
2.106
2.589
2.991
3.326
3.605
3.837
4.031
4.193
4.327
4.439
4.533
4.611
4.675
4.730
4.775
4.812
4.844
4.870
4.948
4.979
0.806
1.457
1.981
2.404
2.745
3.020
3.242
3.421
3.566
3.682
3.776
3.851
3.912
3.962
4.001
4.033
4.059
4.080
4.097
4.110
4.147
4.160
0.781
1.392
1.868
2.241
2.532
2.759
2.937
3.076
3.184
3.269
3.335
3.387
3.427
3.459
3.483
3.503
3.518
3.529
3.539
3.546
3.564
3.569
0.758
1.332
1.766
2.096
2.345
2.534
2.678
2.786
2.868
2.930
2.978
3.013
3.040
3.061
3.076
3.088
3.097
3.104
3.109
3.113
3.122
3.124
0.735
1.276
1.674
1.966
2.181
2.339
2.455
2.540
2.603
2.650
2.683
2.708
2.727
2.740
2.750
2.758
2.763
2.767
2.770
2.772
2.776
2.778
Using Microsoft Excel, these are calculated with the function: PV(interest, years, −1).
I NDEX
A. T. Kearney, 673
ABC classification, 518, 538–539, 682
Accenture, 673, 674
Acceptable quality level (AQL), 333–335
Acceptance sampling, 333–335
Accommodation strategies, 207
Accounting function, 639–640
Accurate response, 493
Acquisition costs, 414–415
Activities
changing the sequence of, 285–286
defined, 78
fitting to strategy, 30
parallel, 270, 285
Activity-based costing, 721–723
Activity direct costs, 86
Activity relationship diagram, 174
Activity-system maps, 30–31
Actual customer contact, 207
Adaptive control, 711
Adaptive forecasting, 453
Additive seasonal variation, 458
Adjacency patterns, 174
Advanced Optical Components, 495
Advanced planning, 692
After-sale support, 28
Aggregate operations plan, 490, 492–496;
See also Sales and operations
planning
Agile supply chains, 407
Air, as a transportation method, 380
Airline industry
learning curves and, 130
use of straddling, 29
yield management, 503–505
Aisle characteristics, 184
Alibaba.com, 265
Alliance and partnerships, 74, 353,
470–471
Alternative path structures, 229
Amazon, 3, 14, 265, 311
Ambient conditions, 184
AMD, 411
American Airlines, 504
American Express, 679
American Hospital Association, 658
Amortization, 719
Ampere, Inc., 567
Analytics, business, 13
Annuity, 726–728
ANSI/ASQ Z1.4-2003, 311
A.P. Moller-Maersk Group, 110
APICS, 379
APICS Supply Chain Council, 436
744
Apple Computer, 14, 43, 44, 183, 185, 201,
402, 671
Appraisal costs, 302
AQL, 333–335
Arm’s length relationships, 409
Arrival patterns, 226
Arrival rate, 121, 224
Arrival variability, 207
Arrivals, 223; See also Waiting line analysis
Artifacts, 185
Assemble-to-order, 150
Assembly charts (gozinto), 155–156
Assembly drawing, 155
Assembly line
balancing of, 175–178
batch sizes, 634–635
defined, 152–153, 170
to deliver services, 212–213
development of, 11
facility layout and, 152–153, 174–175
pacing, 174, 273
Asset turnover, 16–17
Assignable variation, 318
Assignment method, 599–601
Attributes, 325–328
Auction, reverse, 403
Audits, manufacturing, 679–681
Autocorrelation, 447
Automated guided vehicle (AGV), 712
Automated materials handling systems
(AMH), 712–713
Automation
of manufacturing, 712–713
total factory, 715
Available to promise, 562–563
Average aggregate inventory value,
416–417
Avoidable costs, 719
Awards, for quality, 12, 299–300
Backflush, 360
Backorder, 520
Backordering costs, 495
Backward scheduling, 592, 638
Balance, system, 114
Balanced scorecard, 684
Balancing, of assembly lines, 175–178
Balancing loops, 682
Baldrige National Quality Award, 12,
299–300
Balking, 227
Bar chart, 90–91
Bar coding, 540, 593, 603
Base-case financial model, 58–60
Batch arrival, 226
Batch sizes, 634–635
Behavioral science approach, 207–211
Benchmarking, 15, 274, 279, 311–312, 679
Best operating level, 112
Best practices, 310
Bias errors, 464
Bid, request for, 403
Bill of materials (BOM), 563–565, 568–569
Black & Decker, 44, 671
Black belt program, 12, 308
Blocking, 270
Blueprints, service, 211–212, 682
BMW, 27, 113
Boeing, 32, 130, 151, 381, 383
Boston Consulting Group, 673
Bottlenecks
adding capacity to eliminate, 114
analysis of, 682
capacity constrained resources, 628,
632–634, 636–637
defined, 628, 632
drum, buffer, rope, 632–634
finding, 630–631
in hospitals, 662–663
methods for control, 629–637
in multiple-stage process, 270
saving time, 631
BPR Capture, 682
Brain surgery projects, 673–674
Brainstorming, 42, 52
Break-even analysis, 153–155
Breakthrough projects, 74
British Airways, 364
British Petroleum, 32
Brue, Greg, 309
Budgeted cost of work performed (BCWP),
91–92
Budgeted cost of work scheduled (BCWS),
91–92
Budgets, 495
Buffered core, 205
Buffering, 270, 275, 276, 632–634
Bullwhip effect, 404–405
Bundling, product-service, 9
Burger King, 271–273
Business analytics, 13
Business process reengineering (BPR), 12,
684–686
c-charts, 328–329
CAD, 52, 713–714
Campbell Soup, 404–405
Canon, 47
745
INDEX
Capability index, 322–325
Capability sourcing, 410
Capability variability, 207
Capacity
defined, 112, 628
overutilization, 360
unbalanced, 626–628
underutilization, 360
Capacity-constrained resources (CCR),
628, 632–634, 636–637
Capacity cushion, 115
Capacity management, 110–129
changing capacity, 114–115
decision trees, 117–120, 683
defined, 111
determining requirements, 115–117
economies of scale, 110, 112–113
flexibility of, 113
focused factory, 113
hospitals, 660–661
intermediate range, 111
long range, 111
objective of, 111
restaurant example, 281–283
in services, 120–122, 203–204,
281–285
sharing of, 114
short range, 111
strategic, 111
time dimensions of, 111
Capacity utilization rate, 112, 121
Capital, cost of, 723–726
Capital asset pricing model (CAPM), 725
Capital equipment; See Equipment
Care chains, 659–660
Careers, in OSCM, 9–10
Carrying costs, 519, 635
Cash flows, 58–60, 625, 639
Cash-to-cash cycle time, 436–439
Causal forecasting, 446
Causal loops, 682, 683
Causal relationship forecasting, 466–468
Cause-and-effect diagrams, 305, 307, 682
Cell layout, 152, 170, 181–182, 713
Central America Free Trade Agreement
(CAFTA), 382
Centroid method, 384, 387–388
Certification, quality, 12, 310–312
Champions, 308, 309
Changeover time, 356, 363
Chase, R. B., 207
Chase strategy, 494
Checksheets, 305, 306
Chief Operating Officer (COO), 10
Chrysler, 311
Cincinnati Milacron, 713
Circulation paths, 184
Classic accommodation strategy, 207
Classic reduction strategy, 207
Clinical dashboard, 665
Cloud computing, 426
Coca-Cola, 411
Collaborative planning, forecasting, and
replenishment (CPFR), 470–471
Common stock, cost of, 725
Common variation, 318
appraisal, 302
avoidable, 719
backordering, 495
capital, 723–726
carrying, 519, 635
development, 60
external failure, 302
fixed, 718
holding, 495, 519
indirect, 86
internal failure, 302
inventory, 495, 519–520
opportunity, 719
ordering, 520
overhead, 721–723
ownership, 414–416
prevention, 302
versus price, 27
production, 495
quality, 301–303
setup, 363, 519, 635
sunk, 718–719
variable, 718
CPFR, 470–471
Cpk, 322–325
CPM, 78–85, 684
Cradle-to-grave, 25
Crashing, project, 86–89
Creation of service, 203
Creative Output, 623
Creativity, 42
Critical Chain Project Management, 638
Critical customer requirement (CCR), 304
Critical path, 79
Critical path method (CPM), 78–85, 684
Critical processes, 285
Critical ratio (CR), 594–595
Critical zone, 121
Crosby, Philip, 299
Cross-docking, 381
Cumulative average time, 131–132
Cumulative standard normal distribution,
522, 529, 738
Customer loyalty analysis, 678
Customer order decoupling point, 149–150,
445, 516, 659
Customer requirements, 50, 304
Customer service dashboard, 665
Customer surveys, 678
Customer value, 14, 351, 353
Customers
accommodation of, 207
arrival of, 223
contact with, 8, 203
in control of process, 209
designing for, 49–51
lean, 354
needs of, 30–31
new role of, 206–207
segmenting, 223
self-service approach, 30–31, 213
touch points for, 14
waiting lines; See Waiting line analysis
Customization, mass, 12
Customized products, 46, 48
Cut-and-try approach, 496–501
Competitive advantage, 382–383
Competitive dimensions, 27–29
Complementary products, 493
Complex systems, 46, 48–49
Complexity, 56
Compound value, 726–727
Computer-aided design (CAD), 52, 713–714
Computer-aided engineering (CAE), 713
Computer-aided manufacturing (CAM), 715
Computer-aided process planning
(CAPP), 713
Computer-assisted diagnosis, 667
Computer graphics, 713
Computer-integrated manufacturing
(CIM), 715–716
Computer Sciences Corporation, 673
Computer simulation; See Simulation
Computerized physician order entry
(CPOE), 664
Concept development, 46, 49
Concurrent engineering, 49, 204, 285
Conformance quality, 61, 301
Consolidation warehouses, 381
Constant arrival distribution, 224
Consulting, 671–690
defined, 672
economics of, 673–674
industry, 673
manufacturing consulting areas, 674
need for, 674–675
process, 676–684
for services, 675
tool kit, 677
Consumer’s risk, 333
Container system, 361
Continental Airlines, 29
Continuous improvement, 624, 682
Continuous process layout, 153
Continuous replenishment, 404
Continuous simulation models, 244–245
Contract manufacturers, 43–44, 408
Control charts
continuous improvement, 682
defined, 305
features of, 307
for process monitoring, 321
for project management, 90–91
Control limits, 329–330
Core competencies, 43–44, 409–410
Core goods/services, 8–9
Corporate goals, 286
Correlation analysis, 683
Cost accounting, 639
Cost activity pools, 721
Cost avoidance, 51
Cost drivers, 721
Cost of goods sold, 416–417
Cost of quality (COQ), 301–303
Cost schedule status report (CSSR), 91
Cost trade-off decision, 222
Costing rules, 91
Costs
acquisition, 414–415
activity-based, 721–723
activity direct, 86
to add capacity, 114
746
INDEX
Cycle counting, 518, 539–541
Cycle time
cash-to-cash, 436–439
components of, 630
defined, 267, 360
as a performance metric, 275
in a two-stage process, 270
work sampling, 279, 682
workstation, 174
Cyclical scheduling, 661
Daily dispatch list, 602–603
Dashboards, 665, 684
Dasu, Sriram, 207
Data
analysis of, 312, 682–683
gathering of, 679–681
Data analytics, 13
Data envelopment analysis, 683
Data integration, 431
Data integrity, 602–603
Data responsibility, 603
Data warehouse, 431
Days-of-supply, 276
Debt, 724–725
Decision making, break-even analysis
and, 153–155
Decision points, 268–269
Decision rules, 176
Decision support, 428–429
Decision trees, 117–120, 683
Declining-balance method, 720
Decomposition, 458–463
Decoupling point, 149–150, 445, 516, 659
Defects, 298, 303–304, 309; See also
Quality
Defects per million opportunities (DPMO),
61, 304
Define, measure, analyze, improve, and
control (DMAIC), 304–305
Delivery
defined, 7
reliability and speed of, 28
Dell Computer, 114, 150, 168
Deloitte & Touche, 672
Delphi method, 469–470
Demand
changes in, 28
components of, 447
dependent, 520–521
economies of scale, 110, 112–113
independent, 520–521
for product, 563
uncertainty of supply and, 405–407
volatility of, 120–121
Demand management, 567–568; See also
Forecasting
Demand-pull scheduling, 366
Deming, W. Edwards, 299
Dependent demand, 520–521
Dependent events, 627
Depreciation, of capital equipment, 719–721
Depreciation-by-use method, 720–721
Derivative projects, 74
Design for manufacturing and assembly
(DFMA), 52–56, 204
Design of experiments (DOE), 308
Design of jobs; See Job design
Design of products; See Product design/
development
Design quality, 27–28, 61, 300–301
Development cost, 60
DFMA, 52–56, 204
DHL, 379
Diagnosis-related groups (DRGs), 664–665
Diary studies, 682
Dimensions of quality, 301–302
Direct distribution, 516
Direct observation, 279
Direct-to-store approach, 516
Discounted cash flow, 729
Discrete distribution, 226
Discrete simulation models, 244–245
Diseconomies of scale, 112–113
Dispatching, 593
Distribution; See also Warehouses
of arrivals, 224
direct, 516
exponential, 225
poisson, 225–227, 328
service time, 228
Distribution center bypass, 516
Divergence, 56
Divisibility, 692
DMAIC, 304–305
DOE, 308
Dollar days, 637
Double-declining balance method, 720
DPMO, 304
Drum, 632–634
DuPont, 78
Dynamic programming, 692
E-commerce, 12
E-procurement, 353
Earliest due date first rule, 596
Early adopter, 716
Early start schedules, 80–81, 83
Earned value management (EVM), 91–94
Earning rules, 91
eBay, 207
Ecodesign, 54–56
Economic analysis, of new projects, 57–61
Economic order quantity (EOQ), 524,
572–574
Economic prosperity, 25
Economics of waiting lines; See Waiting
line analysis
Economies of scale, 110, 112–113
Economies of scope, 114
Effectiveness, 14, 25–26
Efficiency, 14–17, 274
Efficient supply chains, 407
Effort variability, 207
Einstein, Albert, 726
Electronic commerce, 12
Electronic data interchange (EDI), 404
Electronic Data Systems, 673
Electronic medical records, 666
Eli Lilly, 404
Employee scheduling, 605–607, 661
Employee surveys, 679
Engineer-to-order, 150–151
Enrichment, job, 278–279
Enterprise resource planning (ERP), 426–443
cash-to-cash cycle time, 436–439
in the cloud, 426
decision support and, 428–429
defined, 427
evaluation of effectiveness, 435–439
example, 432–435
integration of business functions and,
429–431
major vendors, 427
SAP, 427, 433–435
software features, 428
Environment
ecodesign, 54–56
green sourcing, 411–413
ISO 9000/14000, 310–312
Environmental footprint, 349
Environmental stewardship, 25
EOQ, 524, 572–574
Equal contribution line, 694
Equipment
break-even analysis, 153–155
capacity planning and, 115–117
depreciation of, 719–721
economic life of, 719
general/specific purpose, 153
minimizing downtime of, 112
Equity securities, 724
Errors
versus defects, 309
in forecasts, 463–466
gap, 661
task/treatment, 209
Ethics, 210
Event management, 664
Event simulation, 245
Event triggered, 524
Everyday low price, 404
Evidence-based medicine (EBM), 665
Evolve Software, 684
Evolving supply process, 406–407
Executive judgment, 469
Executive leaders, 308
Expected value, 719
Expediting, 86, 593
Experience curves; See Learning curves
Explicit objective, 692
Explicit services, 202
Explosion process, 566–567
Exponential distribution, 225
Exponential smoothing, 452–454
Extent of contact, 203
External benchmarking, 311–312
External failure costs, 302
Face-to-face contact, 206
Facility layout, 168–200
assembly line; See Assembly line
basic formats, 170
continuous process, 153
flexible lines, 179–180
functional, 170
hospitals, 659–660
inputs to, 169
747
INDEX
job shop, 151, 170
lean, 357–358
manufacturing cell, 152, 170, 181–182, 713
mixed-model line balancing, 179–180
office layout, 185
product-process matrix, 153
project layout, 151, 170, 181–182
retail sector, 183–185
spatial, 184
systematic layout planning, 174–175, 659
u-shaped layouts, 179
workcenter, 151–152, 170–174
Facility location, 381–390
Factor-rating system, 384
Factory of the future, 715
Factoryless goods producers, 402
Fail-safe procedures, 309–310
Fail-safing, 211–212
Failure mode and effect analysis (FMEA),
305, 308
FCFS, 228, 596–597
Federal Express, 28, 365, 379, 409
Feedback, 686
Finance function, ERP and, 430
Financial analysis, 718–733
activity based costing, 721–723
base-case model, 58–60
cash flows, 58–60, 625, 639
choosing investment proposals, 723–729
concepts, 718–721
debt, 724–725
effects of taxes, 723
elements of, 625
net present value (NPV), 58–60, 729
ranking investments, 729–730
return on investment (ROI), 625, 639
Financial ratios, 15–17
Finders, of new business, 673
Finished goods inventory, 271, 518
Finite loading, 592
Finite population, 224
First Bank/Dallas, 364
First come, first served (FCFS), 228,
596–597
First-hour principle, 606–607
First party certification, 311
Fishbone diagrams, 305, 307, 682
Fitness for use, 301
Five forces model, 679
5 Ps of production, 674
Fixed costs, 718
Fixed-order interval system, 524
Fixed-order quantity model, 517, 524–532
Fixed-order quantity systems, 664
Fixed-time period model, 518, 524–526,
532–534
Fixed-time period systems, 664
Flexibility
capacity, 113
in product development, 28
Flexible line layouts, 179–180
Flexible manufacturing systems (FMS), 711,
713–714
Flexible plants, 113
Flexible processes, 113–114
Flexible scheduling, 661
example, 90
for project management, 684
shop-floor control and, 601–602
tracking, 95
Gap analysis, 679–680
Gap errors, 661
Geddes, Patrick, 24
Gemini Consulting, 673
General Electric, 298, 303
General Motors, 32, 311, 404, 492
General purpose equipment, 153
Global enterprise resource planning
systems, 13
Global logistics, 379
Go/no-go milestones, 57
Goal programming, 692
Goals
clear, 686
corporate, 286
of the firm, 625
of TQM, 299
Goldratt, Eli, 622–625, 638
Goldratt Institute, 624
Good housekeeping, 364
Goods, versus services, 7–8
Goods-services continuum, 8–9
Google Cardboard, 49
Gozinto, Zeparzat, 167n
Gozinto chart, 155–156
Graphical linear programming, 693–695;
See also Linear programming
Gray hair projects, 673
Green belt program, 12, 308–309
Green sourcing, 411–413
Greenfield, Karl Taro, 258
Grinders, 673
Gross requirements, 567, 570
Group technology, 170, 358, 591
Grouping-by-association philosophy, 184
Flexible workers, 114
Flextronics, 408
Flow design, 155–157
Flow of service experience, 207
Flow-shop layout, 170
Flow time
defined, 275
Little’s law and, 277–278
reduction of, 285–287
Flowcharting
as analytical tools, 305, 306
process, 156–157, 268–269
service blueprints and, 211–212, 682
use of, 682
FMEA, 305, 308
Focused factory, 113
Ford, Henry, 11–12, 351
Ford Motor Company, 42, 112, 311, 312
Forecast including trend, 453–454
Forecasting, 444–488
adaptive, 453
capacity planning, 115–117
causal, 446, 466–468
components of demand, 447
CPFR, 470–471
demand management, 567–568
errors in, 463–466
historical analogy, 469
market research, 469
panel consensus, 469
purpose of, 445
qualitative techniques, 446, 468–470
selecting method, 448–449
strategic, 445
tactical, 445
time series analysis, 448–463
decomposition of, 458–463
defined, 446
exponential smoothing, 452–454
linear regression analysis, 455–458
simple moving average, 449–451
weighted moving average, 451–452
trend, 447–448, 453–454
types of, 446
use by consultants, 683
web-based, 470–471
Forward buying, 404
Forward scheduling, 592, 638
Foxconn, 402
Free trade zone, 382
Freeze window, 359
Frito-Lay, 714
Frozen, 562–563
Fujitsu, 410
Functional layout, 170
Functional managers, 76
Functional products, 405–407
Functional projects, 75–76
Functional silo, 435–436
Functionality, 184
Funnel, process as a, 287
Gantt, Henry L., 90
Gantt chart
development of, 79
drawback of, 79
Hackers Computer Store, 117–120
Hand delivery, 381
Hardware systems, 711–713
Health care operations management,
656–670
capacity planning, 660–661
care chains, 659–660
classification of, 658
defined, 657
inventory management, 664–665
layout, 659–660
performance measures, 665
quality management, 661–663
scheduling, 590–591, 661
supply chains, 663–664
trends, 665–667
Health information exchanges (HIEs),
666–667
Hedging supply chains, 407
Heterogeneous process, 8
Hewlett-Packard, 334, 404, 409
High degree of customer contact, 203, 204
High-risk products, 46, 48
Highway, 380
Hill, Terry J., 29
Histograms, 305
748
INDEX
Historical analogy, 469
Hitachi, 410
Holding costs, 495, 519
Home Depot, 184
Homogeneity, 692
Hon Hai Precision Industry, 402
Honda Motors, 43, 112, 266
Honeywell, 364
Horizontal job enlargement, 278–279
Hospitality (hotel) industry, 213–215
Hospitals, 656–670
capacity planning, 660–661
care chains, 659–660
classification of, 658
defined, 657
inventory management, 664–665
layout, 659–660
performance measures, 665
quality management, 661–663
scheduling, 590–591, 661
supply chains, 663–664
trends, 665–667
House of quality, 50–51
Housekeeping, good, 364
Hub-and-spoke systems, 381
Human resources, ERP and, 430–431
Hybrid process, 271–272
Hypothesis testing, 683
IBM, 9, 404, 673
IDEO, 42–43, 49
Idle time, 630
IKEA, 30–31, 69–71, 184
Immediate predecessors, 79–80
Impatient arrival, 227
Implicit services, 202
In-transit inventory, 518
Independent demand, 520–521
Indirect costs, 86
Indirect observation, 279
Individual learning, 131, 138–139
Industrial design, 49
Industrial robots, 667, 711–712
Infinite loading, 591
Infinite population, 223–224
Infinite potential length, 227
Information systems, 94–95
Infosys Technology, 673
Initiatives, 26
Innovation, 205–206
Innovative products, 406–407
Input/output control, 602–603
Inputs, 111, 169
Inspection, 309
Institute for Health Care Optimization, 656
Intangible assets, 719
Intangible processes, 7–8
Integer programming, 692
Integrated medical care, 665
Integrated supply chain metrics, 436–438
Intel, 409–411
Interest rate, 726
Interest tables, 740–743
Intermediate range capacity
management, 111
Intermediate-range planning, 491–492
Internal failure costs, 302
Internal rate of return, 729–730
Internal sourcing agents, 412
International logistics, 379; See also
Logistics
International Organization for
Standardization, 12, 310
Internet; See also Technology
e-procurement, 353
electronic commerce, 12
electronic data interchange (EDI), 404
web-based forecasting, 470–471
Interworkcenter flows, 171–173
Inventory
accuracy of, 538–541
buffer, 270, 275, 276, 632–634
costs, 495, 519–520
days-of-supply, 276
defined, 518, 625
finished goods, 271, 518
in-transit, 518
purposes of, 518–519
turnover of, 16–17, 276, 416–417,
534–535
types of, 517
vendor managed, 404
work-in-process, 179, 271, 276, 518
Inventory management, 515–558
ABC classification, 518, 538–539, 682
bar coding, 540, 593, 603
cycle counting, 518, 539–541
fixed-order quantity models, 517,
524–532
fixed-time period models, 518, 524–526,
532–534
hospitals, 664–665
independent versus dependent demand,
520–521
multiperiod systems, 524–525
price-break models, 535–538
RFID, 540, 593, 660
safety stock; See Safety stock
single-period model, 517, 521–524
Inventory on hand, 492
Inventory position, 526
Inventory records, 565–566, 569
Inventory replenishment, 404, 471
Inventory transactions file, 566
ISO 9000/14000, 12, 310–312
Iso-profit line, 694
ISO/TS 16949, 311
Issue trees, 677–678
Jaguar, 112
Japanese Railways, 679
JC Company, 496–501
J.D. Power and Associates, 301
JDA Software, 427
Job design
behavioral considerations in, 278–279
decision to make, 278–280
defined, 278
specialization of labor, 278
work measurement, 279–280
Job enrichment, 278–279
Job sequencing, 594–595
Job shop, 151, 170
Job standards, 279–280
Johnson’s rule, 594, 598–599
Joint business planning, 471
Jones, D. T., 364
Judging encounter performance, 207
Juran, Joseph M., 299, 301
Just-in-time (JIT); See also Lean
production/manufacturing
defined, 11
evolution of, 351
in hospitals, 665
mixed-model line balancing, 179–180
production, 359
versus synchronous manufacturing,
638–640
Kaizen, 356
Kanban, 360–363
Kanban pull system, 360
Kawasaki, 361
Kelley, David M., 42
Key process dashboard, 665
Kmart, 184
Labor, specialization of, 278
Labor-limited process, 592
Labor productivity measures, 15–16
Land’s End, 4
Largest-number-of-following-tasks rules,
177–178
Last-come, first-served, 595
Late start schedules, 80–81, 83
Launch, of new products, 45, 46
Layout, facility; See Facility layout
Lead time, 149
Leaders, executive, 308
Lean customers, 354
Lean layouts, 357–358
Lean logistics, 354
Lean procurement, 353
Lean production/manufacturing; See also
Manufacturing
defined, 150, 351
design principles, 357–364
evolution of, 11–12
JIT and, 308
kanbans, 360–363
lean layouts, 357–358
make-to-stock and, 150, 271–273
minimized setup time, 363
outcome of, 353–354
overview of, 351–352
scheduling and, 359–363
versus theory of constraints, 624
Toyota Production System, 352–353
value stream mapping, 276, 355–357
Lean services, 364–366
Lean Six Sigma, 308
Lean suppliers, 353
Lean supply chains, 353–354, 363–364
Lean warehousing, 354
Learning curves, 130–146
assumptions of, 131–132
defined, 131
individual learning, 131, 138–139
749
INDEX
managerial considerations, 140
organizational learning, 131, 139–140
plotting of, 132–138
tables, 133–137
Learning percentage, 138
Least-slack rule, 594
Least square regression analysis, 455–458,
461–463
Least total cost (LTC), 572, 574
Least unit cost, 572, 574–576
Level schedule, 359–360
Level strategy, 494
Life cycle, product, 55, 206
Limited line capacity, 227
Limited resources, 692
Line structure, 228–229; See also Waiting
line analysis
Linear programming, 691–710
applications, 691–692
defined, 691
graphical, 693–695
model, 692–693
transportation method, 384–387, 599
using Excel, 695–698
Linear regression forecasting, 455–458
Linearity, 692
Liquid, 562–563
Little’s Law, 277–278
L.L. Bean, 4, 679
Lockheed Martin, 151
Logistics, 378–401; See also Warehouses
cross-docking, 381
decision areas, 380–381
defined, 283, 379, 408
ERP and, 430
example, 283–285
facility location criteria, 381–383
green sourcing and, 411–413
international, 379
lean, 354
outsourcing of, 408–409
plant location methods, 383–388
third-party providers, 379, 408, 663
Logistics-System Design Matrix, 380
Long range capacity management, 111
Long-range planning, 491–492
Long-term debt, 724–725
Long term forecasting, 448
Loss function, 320
Lot-for-lot (L4L), 572–573
Lot size, 335, 572–576
Lot tolerance percent defective (LTPD),
333–335
Low-cost accommodation, 207
Low degree of customer contact, 203, 204
Low-level coding, 565
Lower control limit (LCL), 326–332
Loyalty, customer, 678
versus synchronous manufacturing,
638–640
system structure, 563–567
Matrix projects, 76–77
McDonald’s, 12, 52, 212–213, 221, 266,
271–273, 365, 366, 384
McKinsey & Company, 673, 676
Mean, 318
Mean absolute deviation (MAD), 464–466
Mean absolute percent error (MAPE),
465–466
Mean squared error, 464
Measurement by attributes, 325–328
Medium term forecasting, 448
Merchandise groupings, 185
Metrics, 91, 273–275
Microsoft, 30, 94, 427
Microsoft Project, 684
Milestone chart, 90–91
Miller Brewing Company, 364
Minders, 673
Minimum-cost scheduling, 86
Mixed line structure, 229
Mixed-model line balancing, 179–180
Mixed strategy, 494
Mixed virtual customer contact, 207
M&M Mars, 112
Modular bill of materials, 564
Motivation, 138
Motorola, 303, 321, 404
Moving average, 449–452
Multichannel, multiphase line structure, 229
Multichannel, single phase line structure,
228–229
Multifactor productivity measure, 34
Multiperiod inventory systems, 524–525
Multiple lines, 227
Multiple regression analysis, 468
Multiple-stage processes, 270
Multiple-to-single channel structures, 229
Multiplicative seasonal variation, 458
Multivariate testing, 308
Musk, Elon, 23
Machine-limited process, 592
Machining centers, 711
Maintenance, preventive, 358
Maister, David H., 673
Make-to-order, 150–151, 271–273
Make-to-stock, 150, 271–273
Making, 7
Malaysian Airlines, 208
Malcolm Baldrige National Quality Award,
12, 299–300
Management efficiency ratios, 15–17
Managers, 74
Manpower, 366
Manufacturing
audit of, 679–681
automation, 712–713
CAM, 715
capacity planning; See Capacity
management
CIM, 715–716
consulting areas, 674
contract, 43–44, 408
DFMA, 52–56, 204
ERP and, 430
FMS, 711, 713–714
JIT; See Just-in-time (JIT)
lean; See Lean production/manufacturing
manufacturing execution systems
(MES), 591
plant location methods, 383–388
process analysis; See Process analysis
robot use, 667, 711–712
scheduling; See Scheduling
synchronous, 624–625, 634, 638–640
technology in, 711–715
Manufacturing cell, 152, 170, 181–182, 713
Manufacturing execution systems (MES), 591
Manufacturing inventory, 518
Manufacturing planning and control
systems (MP&CS), 714
Manufacturing processes, 148–167
break-even analysis, 153–155
customer order decoupling point, 149–
150, 445, 516, 659
flow design, 155–157
organization of, 151–155
overview of, 149–151
types of, 593
Manufacturing strategy paradigm, 11
Marginal cost, 723
Market-pull products, 46
Market research, 469
Market risk, 716
Marketing function, 639–640
Marketing-operations link, 29–30
Mass customization, 12
Master black belt, 308
Master production schedule (MPS), 561–
563, 568, 636
Material handling, 174, 181, 712–713
Material requirements planning (MRP),
559–589
applications, 560–561
benefits of, 560–561
bill of materials (BOM), 563–565,
568–569
computer programs, 566–567
defined, 560
example using, 567–572
lot sizing, 335, 572–576
master production schedule, 561–563,
568, 636
scheduling and, 592
NAFTA, 382
Nakamura, Toshihiro, 169
National Institute of Standards and
Technology, 12
NEC, 410
Net change systems, 567
Net income per employee, 15
Net present value (NPV), 58–60, 729
Net profit, 625, 639
Net requirements, 567, 570
Net return, 723
Netflix, 207
Network, supply, 4–5
Network-planning models
critical path method, 78–85, 684
time-cost models/crashing, 86–89
New product development; See Product
design/development
Newsperson problem, 521–524
Nightingale, Florence, 662
Nissan, 112
Non-steady state, 282
750
INDEX
Nonbottleneck, 628; See also Bottlenecks
Nonlinear programming, 692
Nonpaced production process, 273
Nordstrom Department Stores, 213–214
North America Free Trade Agreement, 382
NTN Driveshafts Inc., 381
Numerically controlled machines, 711
Objective function, 694
Objectives
of capacity management, 111
stretch, 309
Obsolescence, 521, 719
Office Depot, 30
Office layout, 185
OfficeMax, 30
Ohno, Tai-ichi, 351
Online catalogs, 403
Operating characteristic curves, 334–335
Operating cycle, 436
Operating expenses, 625–626
Operation and route sheet, 155–156
Operation time, 275
Operational design decisions, 58
Operational risks, 716
Operations, 4
Operations and supply chain management
(OSCM)
careers in, 9–10
categorizing of processes, 6–7
current issues, 13–14
defined, 3
development of, 11–14
professional societies for, 10
services versus goods, 7–8
supply network, 4–5
Operations and supply chain strategy,
23–41
agile supply chains, 407
competitive dimensions, 27–29
defined, 25–26
efficient supply chain, 407
fitting activities to strategy, 30
at IKEA, 30–31
order winners/qualifiers, 29–30
production planning, 493–494
productivity measurement, 33–35
responsive supply chains, 407
risk and, 31–33, 333, 683, 716
risk-hedging supply chains, 407
sustainability strategy, 13, 24–25
trade-offs, 29
Operations consulting, 671–690
defined, 672
economics of, 673–674
industry, 673
manufacturing consulting areas, 674
need for, 674–675
process, 676–684
for services, 675
tool kit, 677
Operations effectiveness, 25–26
Operations scheduling; See Scheduling
Operations technology, 711–717; See also
Technology
Opportunity costs, 719
Opportunity flow diagrams, 305, 307
Optima!, 682
Optimal order quantity Qopt, 527–529
Optimized production technology (OPT), 624
Oracle, 427
Order qualifiers/winners, 29–30
Ordering costs, 520
Organization, of production processes,
151–155
Organization charts, 155, 682
Organizational learning, 131, 139–140
Organizational risks, 716
Outputs, 34, 111
Outsourcing
benefits, 408
capacity planning and, 114–115
contract manufacturers, 43–44, 408
defined, 408
drawbacks to, 409
growth of, 13
of logistics, 408–409
reasons to, 408
supplier relationships, 409–411
Overhead costs, 721–723
Overutilization, 360
Ownership costs, 414–416
p-charts, 326–327
P-model, 524
Pacing, 174, 273
Package of features, 8
Panel consensus, 469
Parallel activities, 270, 285
Parallel workstations, 179
Pareto, Vilfredo, 538
Pareto analysis, 682
Pareto charts, 305, 306
Pareto principle, 538
Partial factor productivity, 274
Partial productivity measure, 34
Partnerships, 74, 353, 470–471
Patient arrival, 226–227
Payback period, 729
Payoff analysis, 683–684
Peg record, 566
People Express, 504
Perceived quality, 300–301
Performance dashboards, 665, 684
Performance measurement
benchmarking, 15, 274, 279, 311–312, 679
dollar days, 637
financial; See Financial analysis
hospitals, 665
operational measurements, 625–626
process analysis, 273–275
product development, 61
productivity measures, 12, 33–35, 274, 626
of sourcing, 416–417
using ERP, 435–439
work measurement, 279–280
Period cash flow, 59
Periodic review system, 524
Periodic system, 524
Perishable process, 8
Permeable system, 205
Perpetual system, 525
Personal-attention approach, 213–215
Personnel scheduling, 605–607
PERT, 78–79, 83, 684
Peters, Tom, 75
Phase zero, 46
Phillips, 32
Physician-driven service chains, 664
Pipeline, 381
Pittiglio Rabin Todd & McGrath, 671–672
Planned-order receipts, 567, 570
Planned-order release, 567
Planned value (PV), 91
Planning; See also Operations and supply
chain strategy
for capacity; See Capacity management
ERP; See Enterprise resource
planning (ERP)
operations and supply chain strategy, 26
process of, 6–7
product development, 46
production, 493–494
strategic, 26
Plant location methods, 383–388
Plant tours, 679–681
Plant within a plant (PWP), 113
Platform products, 46, 47–48
Poisson distribution
arrivals and, 225–227
process control, 328
Poka-yokes, 212–213, 309–310
Porter, M. E., 31, 680
Precedence relationship, 175
Predetermined motion-time data systems
(PMTS), 279
Present value (PV), 726–728, 736
Prevention costs, 302
Preventive maintenance, 358
Price
versus cost, 27
everyday low, 404
sales, 60
Price-break models, 535–538
Primavera, 94–95
Primavera Project Planner, 684
Priority rules, 228, 595–601
Probability analysis, 86–89
Probability approach, 529
Probability of reservice, 230
Problem analysis, 682
Problem definition tools, 677–679
Problem-solving groups, 364
Procedures projects, 673
Process analysis, 266–297
examples, 280–287
flow time reduction, 285–287
Little’s law, 277–278
make-to-stock, 150, 271–273
measuring performance, 273–275
multiple-stage process, 270
production process mapping, 275–278
single-stage process, 270
slot machine example, 266–269
Process batch, 634–637
Process capability, 321–325; See also
Statistical process control (SPC)
Process change, 74
751
INDEX
Process control charts, 305, 307
Process control procedures, 325–332
Process dashboards, 684
Process flow design, 155–157
Process flowcharting, 156–157
Process improvement, 661–663
Process-intensive products, 46, 48
Process mapping, 275–278
Process optimization, 692
Process plans, 714
Process quality, 27–28
Process selection, 151
Process velocity, 275
Processes
categorizing of, 6–7
characterizing, 270
control of, 209
critical, 285
defined, 266
flexible, 113–114
flowcharting of, 156–157, 268–269
as funnel, 287
hybrid, 271–272
multiple-stage, 270
operations versus supply chain, 4–6
serial, 273, 285
service; See Service processes
single-stage, 270
Processing time, 630
Procter & Gamble, 311, 404
Procurement, lean, 353
Producer’s risk, 333
Product change, 74
Product design/development, 42–72
brainstorming, 42, 52
concept development, 46, 49
contract manufacturers, 43–44
creativity, 42
DFMA, 52–56, 204
ecodesign, 54–56
economic analysis of projects, 57–61
flexibility, 28
launch of new products, 45, 46
measuring performance, 61
process, 44–49
role of customers, 49–51
service products, 56–57
testing and refinement phase, 46
value analysis, 51–52
Product launch, 45, 46
Product learning, 131
Product life cycle, 55, 206
Product-process matrix, 153
Product-service bundling, 9
Product structure file, 564, 568–569
Product support, 28–29
Product tree, 564
Production activity control, 601
Production change costs, 519
Production-line approach, 212–213
Production planning, 493–494
Production planning strategies, 494
Production process mapping, 275–278
Production pull system, 352
Production ramp-up, 46
Production rate, 492
external benchmarking, 311–312
gap errors, 661
hospitals, 661–663
house of quality, 50–51
importance of, 634
inspection, 309
ISO standards, 12, 310–312
job enrichment and, 278–279
Malcolm Baldrige Quality Award, 12,
299–300
process, 27–28
QFD, 50–51
reengineering and, 685
of service, 121, 661–663
versus service, 27–28
Shingo system, 309–310
Six-Sigma
analytical tools for, 305–308
defined, 12, 298, 303
lean, 308
methodology, 304–305
process capability and, 321–325
roles and responsibilities, 308–309
versus theory of constraints, 624
specifications, 300–301
statistical process control; See Statistical
process control (SPC)
total quality control, 11
total quality management (TQM)
defined, 299
development of, 12
goals of, 299
versus reengineering, 685
use in hospitals, 661–663
Quality at the source, 301, 358–359
Quality function deployment (QFD), 50–51
Quality Gurus, 299
Quantitative layout techniques, 169, 182
Queue discipline, 228
Queue time, 630
Queues, 223
Queuing systems, 223–230; See also
Waiting line analysis
Queuing theory, 683
Quick-build products, 46, 48
Quick plant assessment (QPA), 680–681
Quill, 30
Production requirements, 497
Production scheduling, 624
Production setup, 181
Productivity, 12, 33–35, 61, 274, 626
Professional service organizations
(PSO), 204
Program Evaluation and Review Technique
(PERT), 78–79, 83, 684
Progress curves, 131
Project, defined, 75
Project crashing, 86–89
Project development time, 60
Project indirect costs, 86
Project layout, 151, 170, 181–182
Project management, 74–109
breakthrough projects, 74
control charts, 90–91
critical chain, 638
defined, 74–75
derivative projects, 74
earned value management, 91–94
functional projects, 75–76
information systems for, 94–95
matrix projects, 76–77
network-planning models
critical path method, 78–85, 684
time-cost models/crashing, 86–89
organizing tasks, 77–78
organizing the team, 75
probability analysis, 86–89
project types, 75–77
pure projects, 75
statement of work, 77
work breakdown structure, 77–78
Project management information systems
(PMIS), 95
Project Management Institute, 94
Project manager, 74, 76
Project milestones, 77
Projected available balance, 570
Prototypes, 46
Pull signals, 665
Pull system, 352
Purchasing function, measurement of, 435
Pure goods/services, 8–9
Pure project, 75
Pure strategy, 494
Pure virtual customer contact, 207
Push systems, 665
Q-model, 524
QFD, 50–51
QS-9000, 311
Quadratic programming, 692
Qualitative forecasting techniques,
446, 468–470
Quality
acceptable quality level (AQL), 333–335
certification, 12, 310–312
continuous improvement, 624, 682
cost of, 301–303
defects, 298, 303–304, 309
defined, 61
design, 27–28, 300–301
dimensions of, 301–302
DPMO, 304
R-chart, 329–332
Radio frequency identification (RFID), 540,
593, 660
Rail, as a transportation method, 380
Raisel, Ethan M., 676
Random errors, 464
Random variation, 318, 447
Randon order rule, 595
Rate cutting, 279
Rate fences, 504
Rath and Strong Consulting, 209
Ratios, financial, 15–17
Raw materials, 518
Reactive system, 205
Real time, 431
Receivables turnover ratio, 16–17
Redbox, 207
Reengineering, 12, 684–686
752
INDEX
Regression analysis, 455–458, 468, 683
Regression model, 389
Reid, Richard A., 654n
Reinforcing loops, 682
Relative measure, 34
Reliability, 28
Remote diagnosis, 667
Reneging, 227
Reorder point, 528–529
Request for bid (RFB), 403
Request for proposal (RFP), 403
Request variability, 207
Research and development, 74
Reservice, 230
Residuals, 463
Resource inputs, 111
Resources, 592
Respect for people, 353
Responsibility charts, 684
Responsive supply chains, 407
Restaurant industry, 271–273, 281–283
Retail sector
layout, 183–185
self-service model, 30–31, 213
Return on investment (ROI), 625, 639
Returning, 7
Revenue per employee, 15
Reverse auction, 403
Rewards, 309
RFID, 540, 593, 660
Risk, 31–33, 333, 521, 683, 716
Risk-hedging supply chains, 407
Risk priority number (RPN), 305
Ritz-Carlton, 213–215
Roadway Logistics, 409
Robots, 667, 711–712
Rogo, Alex, 622–623
Rope, 632–634
Route sheets, 155–156
Routine service organizations
(RSOs), 204
Routing matrix, 181–182
Ruck, Bill, 37
Run charts, 305, 306, 682
Run time, 274
Ryder, 408
Safety stock
establishing, 529
fixed-order quantity model, 517, 530
fixed-time period model, 518, 524,
533–534
in the health care industry, 665
probability approach, 529
Sales and marketing, ERP and, 430
Sales and operations planning, 490–514
aggregate operations plan, 490,
492–496
applied to services, 501–503
defined, 490
intermediate-range, 491–492
level scheduling, 359–360
long-range, 491–492
overview of, 490–492
production planning environment,
493–494
short-range, 491–492
techniques, 496–503
yield management, 503–505
Sales price, 60
Sampling
acceptance, 333–335
by attributes, 325–328
by variables, 329–332
work, 279, 682
Sampson, Scott, 207
Sam’s Club, 431
SAP, 427, 433–435
Sawtooth effect, 526
SBAR, 661–662
Scalzitti, Gary, 401
Scandinavian Airlines, 185
Scatter diagrams, 682
Scheduled receipt, 570
Scheduling, 590–621
backward, 592, 638
critical path method, 78–85, 684
demand pull, 366
FCFS rule, 228, 595–597
finite loading, 592
forward, 592, 638
functions performed, 593–594
in health care, 590–591
infinite loading, 591
input/output control, 602–603
job sequencing, 594–595
lean production and, 359–363
level, 359–360
manufacturing execution systems, 591
master production, 561–563, 568, 636
material requirements planning
(MRP); See Material requirements
planning (MRP)
minimum-cost, 86
objectives of, 594
on one machine, 595–598
of personnel, 605–607
principles of, 604
priority rules, 228, 595–601
production, 624
set jobs on same number of machines,
599–601
shop-floor control, 593, 601–604
simulation; See Simulation
on two machines, 598–599
workcenter, 591–595
workforce, 661
Scorecard, balanced, 684
Seasonal variation, 458–463
Second Life, 207
Second party certification, 311
Segmented service experience, 208–209
Self-check, 309
Self-service approach to service, 30–31, 213
Sensitivity analysis, 60–61
Sequencing, job, 594–595
Serial process, 273, 285
Service blueprinting, 211–212, 682
Service bookends, 207–208
Service Executive System (SES), 591
Service experience fit, 56
Service facilities, location of, 388–389
Service guarantees, 209–210
Service package, 202
Service processes, 201–220
behavioral science approach, 207–211
blueprinting, 211–212, 682
customer contact, 203
customer encounters, 207–211
designing service organizations, 203–211
Internet and, 206–207
managing variability, 207
nature of, 202–203
personal-attention approach, 213–215
production-line approach, 212–213
service guarantees, 209–210
service-system design matrix, 205–207
well-designed, 215
Service rate, 121, 228
Service recovery, 209
Service-system design matrix, 205–207
Service time distribution, 228
Service triangle, 202
Serviceability, of a product, 300
Services; See also Service processes
aggregate planning and, 501–503
capacity planning and, 120–122, 203–
204, 281–285
classification of, 203
consulting and, 675
design of new, 56–57
versus goods, 7–8
lean, 364–366
personnel scheduling, 605–607
pure, 8–9
versus quality, 27–28
quality of, 121, 661–663
retail layout, 183–185
self-service delivery of, 30–31, 213
Service Execution System (SES), 591
virtual, 206–207
yield management, 503–505
Servicescapes, 183–185
Setup costs, 363, 519, 635
Setup time, 181, 274–275, 363, 630
7-Eleven, 410
Shareholders, 24
Shell Oil Company, 24
Shibaura Seisaku-Sho, 168
Shingo, Shigeo, 309
Shingo system, 309–310
Shop discipline, 603
Shop-floor control, 593, 601–604
Short-range capacity management, 111
Short-range planning, 491–492
Short-term debt, 724
Short term forecasting, 448
Shortage costs, 520
Shortest operating time (SOT), 595
Sigma, 319
Signs, symbols, and artifacts, 185
Simple moving average, 449–451
Simulation
consulting and, 682–683
forecasting and, 446
waiting lines, 239–245
Singapore Airlines, 679
Single arrival, 226
753
INDEX
Single channel, multiphase line structure,
228–229
Single channel, single phase line structure,
228–229
Single-minute exchange of die (SMED), 309
Single-period model, 517, 521–524
Single sampling plan, 333–335
Single-stage process, 270
SIPOC, 305
Situation-Background-AssessmentRecommendation, 661–662
Six-Sigma
analytical tools for, 305–308
defined, 12, 298, 303
lean, 308
methodology, 304–305
process capability and, 321–325
roles and responsibilities, 30